Indefinite Integration Questions and Answers

Express the following equation as a function y = f(x) 3xy + 4y = 1 Impossible because it is not a function. 1 3x+4 Of(x) Of(x) - 2-3 4 ||||| 1-3xy 1-49 O f (x) — ²5-² = 3x

(0.00/1.00 point) 0 of 3 attempts 12x, where a represents the Use a system of linear equations with two variables and two equations to solve. A moving company charges a flat rate of $50, and an additional $7 for each box. A taxi service would charge $12 for each box. In parts (a) and (b) of this question, we determined the cost of the 50+7x and the cost of the taxi service was represented by y = moving company was represented by y number of boxes. What is the minimum number of boxes you need for it to be cheaper to use the moving company? Retry (10 variants)

What substitution is needed to rewrite the equation as a quadratic equation in terms of U? x2/5 +6x¹/5-16 = 0 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a U = x²/5 b U P. U = x¹/5 U=X d U = x²

Consider the function f(x) = − 2x³ + 33x² − 168z + 3. For this function there are three important open intervals: ( — ∞, A), (A, B), and (B, ∞o) where A and B are the critical numbers. Find A and B For each of the following open intervals, tell whether f(x) is increasing or decreasing. (-∞, A): [Select an answer (A, B): Select an answer (B, ∞0): Select an answer

Solve the equation and write the solution set. If there is more than one solution, list them in order from smallest to largest. Do not enter any spaces in the answer. 2 x² = 100

Solve the equation and write the solution set. Use / to write fractions, as in 34/9 means 34. . If there is more than one solution, list them in order from smallest to 9 largest. Do not enter any spaces in the answer. (12x + 1)(x-7)= 0

X T What is the equation for a cosecant function with vertical asymptotes found at x = + n, such that n an integer?

Find equations for two lines that are both tangent to the curve y=x²-3x + 3x - 5 and parallel to the line 3x - y = 1

Find an equation of the normal line to the curve of y = √√x that is parallel to the line 4x + y = 1. y =

A A What is the equation for a cosecant function with vertical asymptotes found at x = 2 2 +-n, such that n is an integer?

Find the derivative of the function using the definition of derivative. 1-4t 3 + t G(t) = G'(t) = State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)

Suppose that the functions g and fare defined as follows. g(x)=x+8 f(x) = (x+3)(x-3) (a) Find (²) (5). (a) 9 (b) Find all values that are NOT in the domain of f If there is more than one value, separate them with commas. 9 (G) (5) = 0 9 (b) Value(s) that are NOT in the domain of 2 -

Evaluate the integral fz³ (zº – 10) dr by making the substitution u = = 6 - 10. I

Evaluate the indefinite integral. √2²√1+z³dz

DETAILS SCALCET9 4.2.012. Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated lis f(x) = x - [1]

Find equations of the spheres with center (1, -3, 4) that just touch (at only one point) the following planes. (a) xy-plane (b) yz-plane (c) xz-plane

Suppose you start at the origin, move along the x-axis a distance of 9 units in the positive direction, and then move downward a distance of 8 units. (x, y, z)=

Consider the quadratic function f(x) = x² - 2x - 8. Determine the following: The smallest x-intercept is x = The largest x-intercept is x = The y-intercept is y =

Solve sin(6x) cos(8x) - cos(6x)sin(8x) =_ - 0.25 for the smallest positive solution. X = Give your answer accurate to two decimal places.

Using Pascal's triangle, find the 4th power of 102. O 108,243,216 0108243212 O 108246216 O 108223216

Solve sin(x) There are two solutions, A and B, with A < B and A and B in radians to 4 decimal places. A = B = - - 0.28 on 0 < x < 2π

Given ● h(x) = f(g(x)) • At x = 4, the equation of the tangent line of f is -5x + y = - 25. • At x = 4, the equation of the tangent line of g is y - 4 = - 8(x-4). Determine h'(4) h'(4) =

Let g(x) = x²√8 + x² Determine the equation of the tangent line to g at (1, 3). Report the solution using slope-intercept form.

Evaluate the indefinite integral. (2x + 1 12²2 -dx x² +1

Evaluate the indefinite integral. (arcsin (a))8 √1-x² -da

Evaluate the indefinite integral. föez sin(e6²) da 6e

Write the inequality in interval notation and graph the interval. 4> -x>-2

Find the vertex form of the function. Then find each of the following. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range s(x) = - 3x² - 24x - 46 s(x) = (Type your answer in vertex form.) (A) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The y-intercept is (Type an integer or decimal rounded to two decimal places as needed.) OB. There is no y-intercept. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ... OA. The x-intercepts are (Use a comma to separate answers as needed. Type an integer or decimal rounded to two decimal places as needed.) OB. There is no x-intercept.

Evaluate the integral by making the appropriate substitution: u = 15 faª (a² − 2)¹5 da = 1 15 fa²¹ (25 – 2)¹5 dx,

Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x)=k, [6,9] k= (Type an exact answer.) The probability density function is f(x) = (Type an exact answer.) ...

m Let x be a continuous random variable over [a,b] with probability density function f. Then the median of the x-values is that number m such that √√ 1/72 S f(x) dx = a the median. f(x) = - 1 128 x, [0,16] The median is m = … Find

3 sec² (t)- 5t2. of f(t) with F(0) = 0. Then Consider the function f(t) Let F(t) be the antiderivative F(t) =

Let f(x) = 15 x² + 1 Enter antiderivative of f(x) Question Help: Video Message instructor + C

A parcel delivery service has contracted you to design a closed box with a square base that has a volume of 9,500 cubic inches. (a) Express the surface area of the box as a function of x. S(x) = _____

Compute the partial sums S₂, S₄, and S₆. 2 + 2/2² + 2/3² + 2/4² + ........... S₂ = ______ S₄ = ______ S₆= ______

Suppose sin(2x) = 3/5. Then sin(x) = _________(If there is more than one possible value, enter the values separated by commas).

Use integration to find f(π), if df/dx= sin(0.6x), and f(0) = 6. Find the total change of f(x) between x = 0 and x = 2, when one df/dx = 4x² + 3x.

Find the displacement of an object on the interval 0 <= t <= 5 if its position s(t) = In(t² +1).

If acceleration is a(t)=In(t²), and v(1) = 2, write an integral function that could be used to find the velocity at any point in time. Do not evaluate the integral.

If acceleration is a(t) = -3t² sin t , and v(1) =10 , write an integral function that could be used to find the velocity at any point in time .Do not evaluate the integral

The velocity of a particle on the time interval [0, 3) is v(t) = cos(2t), where v(t) is in cm/s. Find the average velocity for the interval. If acceleration is a(t) =In(t²), and v(1) = 2, write an integral function that could be used to find the velocity at any point in time. Do not evaluate the integral.

Let f(x) = sin(πx) +2. The graph of f is given below. Determine the following function value. Enter DNE if the function is undefined at x= 0. f(0) =______

Let f(x) = x²+ x + 2 and g(x) = x³ + 2 be polynomials in Z₃[x]. Let I be the ideal generated by f(x) and g(x). Prove that 1∈ I.

Simiplify. sin(θ) + cot(θ)cos(θ) (a)= sin(θ) +______Simplify using cot(θ)=cos(θ)/sin(θ) (b)=(_____________)/sin(θ) Adding using LCD as sin(θ) (c)=___________ Simplify further using cos²(t) + sin²(t) = 1 (d)=__________ Simplify further so the answer has no fraction

Find ∫y+3/y²-7y+12dy for all values of y in the domain of the function, using partial fractions.

For what value of θ is csc θ undefined? a. 90° b. 180° c. 270° d. 315°

Find the exact value, if possible, without a calculator. If it is not possible, use a calculator round to 3 decimal places. #37 tan(sin^(-1)(x - 1)) = a) Let θ = sin^(-1)(x - 1) that means: sin(θ) = b) Using refrence triangle to find tan(θ) =

Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) ∫1/x²-4 dx

Evaluate the indefinite integral by using the given substitution to reduce the integral to standard form. ∫(18r^8 dr) / (√(4 - r^9), u = 4 - r^9.

Evaluate the following integrals. (a)∫4x + 1/ (x-2)(x - 3)²dx (b)∫√x ln(√x) dx (c) x⁵+x+1/x² + 2 dx 2. Let I be the region bounded by the curves y=x², y = 1-x². (a) Give a sketch of the region I. For parts (b) and (c) express the volume as an integral but do not solve the integral: (b) The volume obtained by rotating I about the z-axis (Use the Washer Method. You will not get credit if you use another method). will not get credit if you use another method). (c) The volume obtained by rotating I about the line x = 2 (Use the Shell Method You will not get credit if you use another method).