Definite Integrals Questions and Answers

Evaluate the definite integral r 4 9 7 cos 0 cos 0 Jo de

Let A 0 22 0 2i 0 0 l M3x3 C Given that the eigenvalues of the normal matrix A are 1 i and 3i find the spectral decomposition of A Write each orthogonal projection matrix as a single matrix 1101

Evaluate the definite integral S 1 da x 1 ln x

Evaluate the definite integral 6x 3x 6 e X dx

aluez 2 Pedz dz avec u avec une erreur inf rieure 10 2

6x y dx y 2x 3 dy 0 Final Answer f x y 2y x 3y 6x 2 C

Use the substitution tar integration to transform the integrand into a rational function of t and then evaluate the integral Remember to use absolute values where appropriate Use C for the constant 1 5 15 sin x 8 cos x de

An object moves on a trajectory given by r t 10 cos 4t 10 sin 4t for 0 t How far does it travel The object travels units Type an exact answer using as needed

Find the length of the following two dimensional curve T r t 3 cos t 3t sin t 3 sin t 3t cos t for Osts 2 L 0 Type an exact answer using as needed

Find the length of the following three dimensional curve r t 5 4t 7 3t 1 2t for 1 sts7 L Type an exact answer using radicals as needed

48 From a window 40 feet above the ground in a certain building the angle of elevation to a window in a second building is 43 If the distance between the buildings is 110 feet how far above ground level is the second window If x 40 is the height of the second window what is the first step A tan 43 X 110 B sin 43 X 110 OC sin 43 110 X 110 X D tan 43

42 Draw a diagram and find the remaining part of the right triangle If b 48 and A 36 B O A 144 B 154 OC 54 D 64

Evaluate the integral 2 e 1 2 z e dz x 1 sin x dx

Question 5 of 21 tn or U to make the statement true 2 14 16 9 10 11 12 13 10 12 U se the correct answer below

Show Transcribed Text need help solving the equation confused when it comes to utilizing the trig angles in the equation The final answer should be i t 6 44cos 2pi 10 4

Evaluate b 11 1 11x 3 dx If the integral divereges enter or DNE as appropriate Report EXACT answer if the integral converges Upload your handwritten work in the box below You must show work using proper notation to receive credit for this probl

7 Evaluate the line integral where C is the curve given below 2 Ly ds C3 y 1 0 C x y 1 2 C x 1 m

Evaluate the limit if it exists 1 lim x X 6 I 1 66 X 6

3 Evaluate In 2 e i e 2t j k dt

equation of the line that satisfies the given conditions Through 7 8 perpendicular to the line 2x 5y 8 0 2 54

41 48 Graphing Trigonometric Functions Find the period and sketch the graph 41 y 3 tan x cot x 1 2 43 y 2 cotx 45 y 4 csc 2x 1 x 2 47 y tan 100 42 y tan X 44 y sec 2 46 y tan x an x F 6800 48 y 4 sec 4 x 80

17 20 Fundamental Identities Use the fundamental identities to write the first expression in terms of the second 17 tan t cos t sin t 18 tant sec t cos t 19 tan t sin t t in Quadrant IV 20 sec t sin t tin Quadrant II 21 24 Values of Trigonometric Functions Find the values of the remaining trigonometric functions at t from the given information 12 21 sin t 3 cos t 1 3 22 sin t 1 cos t 0 23 cot t 1 csc t 5 2 3 tan t 0 24 cost 34

The 2014 domestic postage rate for first class letters weighing 3 5 oz or less is 49 cents for th P as a piecewise defined function of the weight x of a letter with 0 x 3 5 Express your a if 0 x 1 if 1 x 2 if 2 x 3 if 3 x 3 5 P x Sketch a graph of this function P 1 20 1 00 0 80 P 1 20 1 00 0 80

ties Pedro has scores of 83 of 75 or greater it Rodro n

f x be a continuous function for which we know and 2 1 6 6 f 2 5 f 6 30 Find the value of the definite integral given by int 2 6 f x 3 f prime x sqrt f x 2 1 d x a a a f x Ida Note as always do not round your answers

e a power senes to approximate the area of the region with an error of less than 0 0001 Use a graphing utility to verify the result Round your answer to four decimal place cost cos x dx r1 cos x dx 0 5 3 A 0 05 x 1 1 0 5 1 2 n 1 05 0 5 1 1 5

Interpret this problem in terms of diffusion Be sure to explain how the Doundary conditions could arise physically 8 u au 8x at au u 0 t C u x 0 0 D K 0 x a 0 t a t 0 0 t ax 0 x a

16 Find the area of the region bounde between and from to y x Y 24 y x x 0 x 2

At a price of 100 there is demand for 860 items and a supply of 500 items At a price of 180 there is demand for 540 items and a supply of 900 items Assuming supply and demand are linear find the equilibrium price and quantity Equilibrium quantity Equilibrium price items

coordinates of a point in the solution set y 1 2 x 4 y x 7

2x 72x 1295 36 x V1 x2 Hint Multiply by the conjugate of the denominator The value of the integral 04450 023 4 dx is

From the relation between the Reimann Sum and the definite integral we see that n 3 14 Im 20 6 lim 7 0 dx 2 n n 8 i 1 and the value of the integral is

1 1 pt Sketch the spiral r 0 sin 0 0 0 T you may use a screenshot of Desmos if you like a 4 pts Determine the exact area that would be enclosed in the portion of the curve in quadrant one

Find all values of the constant a for which the integral x3 1 2 1 dx x Converges Evaluate the integral for these values of a

H Find the length of the curve corresponding to r t 2t e e over the interval 0 t 1 Note the first component is 2t not 2t integor

f x e x and the x axis on the interval 0 In2 about the line x ln2

The area under the curve y 3x4 and above the x axis between x 4 and x 10 is area The area under the curve y 3x4 and above the x axis between x area The area under the curve y 3x4 and above the x axis for x 4 is area 4 and I 100 is

P x et P be a quadratic polynomial such that P 0 1 and x 2x 1 i e a quotient of two polynomials Find the value of the derivative P 0 Justify your answer Hints da is a rational function Write P x ax bx c Then P 0 and P 0 can be expressed in terms of the coefficients a b and c of P What are they Decompose P x x 2x 1 into partial fractions with some unknown constants for the nu merators and see what is the general form of an antiderivative of each of them These antiderivatives are supposed to sum up to a rational function themselves which means that no logarithmic terms are allowed This implies that two of the five unknown constants in the partial fraction decomposition must be zero Finally convert the above partial fraction decomposition into a polynomial equation and compare the coefficients at the corresponding powers x on both sides to find the answer

The region R in the xy plane is bounded by the graphs of y x 1 and y 1 and the lines 2 2 and x 3 If the density of R is 1 the mass of R is given by the integral 3 So m The moment of R about y axis is given by the integral 3 M The moment of R about z axis is given by the integral S 2 M da dr dx Evaluating these integrals the centroid of R is located at T y

1 I and I and just The region R in the cy plane is bounded by the graphs of y 3 sin x y 9 touches the origin The centroid of R is located at T y 2 3

The region R in the xy plane is bounded by the graph of y x 2 the x axis and the lines 0 and x 4 If the density of R is 1 the mass of R is given by the integral 5 0 The moment about the y axis of R is given by the integral m My x y da The moment about the z axis of R is given by the integral M 0 Evaluating these integrals the center of mass of R is located at dx dx

Question 15 5 1 41 BE points O Points 0 of 2 Save Dave borrowed 5900 from his uncle with simple interest of 10 and eventually repaid 7080 principal and interest What was the time period of the loan The time period of the loan was year s Type an integer or a decimal

1 point Consider the following set Calculate the volume of solid shape D V D dedydz D x y z a y 16 a y 4

Consider the differential equation dr 2x A At the point 0 5 1 5 the direction field has a slope of B At the point 1 5 1 5 the direction field has a slope of C Use your answers above to help choose the correct direction field for the differential equation 1 1 N 1 7 1X

C 1 Points webassign net web Student Assignment Responses submit de 1 1 2 DETAILS PREVIOUS ANSWERS SCALCCC5 2 1 0 A graphing calculator is recommended The displacement in centimeters of a particle s moving back and forth along a decimal places a Find the average velocity during each time period

Verify the identity 1 1 cos y 1 1 cos y 1 cot y Use a Pythagorean Identity in the denominator and then use a Reciprocal Identity 1 Use a Pythagorean Identity

y e 5 Oy e 4 Oy In x 4 5 4 v In y 5 3 H 544 3 2 1 N 2 di ba do t 3 4 5 1 2 3 4 5 X

Using the diagram below write BH using at least two other vectors Use only AB AD and AE in your answer 2T E A P F D H G

Evaluate the integrals 1 S tan3xsec xdx

27x y 0 between y 0 and y 2 Let C be the curve 27x y 0 Find the area of the surface generated by revolving C about the y axis Please set up do not evaluate a O 2 54m x 1 2 dx 54 81 5 2 9 0 2 94 b d fy 2 2 v 27 dy 81 dy 81