Indefinite Integration Questions and Answers

Evaluate S 213 10u du 13 10u du Type an Type an exact answer

valuate the following indefinite integral f2dx 2 dx 0 Type an exact answer

Find the centroid of the region above the curve shaded in green in Figure 4 This region is ranges in x from 0 to 600 in from 0 to 430 and above y kx 500 430 400 300 200 100 0 0 y Find centroid of this region 100 200 300 5 400 500 600 430 600 y kx0 7 X 700

Find the volume formed by rotating the region enclosed by x 11y and y x with y 0 about the y axis Volume

Compute the indefinite integral 1 sin x St COS X dx

Evaluate the indefinite integral 3 5 1 de 2 5 1 C

Find one function from the family that constitutes the indefinite integral for s 6x sec x tan x dx

Evaluate the indefinite integral 6x4 5x 23 S dax C

Evaluate the indefinite integral 8x 8x 4x 5 dx C

x 2 x 1 x 2 none of these answers Question 2 Solve for x 3x 1 25 x 0 93 x 2 93 x 1 93 Onone of these answers Question 3 solve for x TO

5 For an elipse that generates the ellipsoid of a lithotripter the major avis has endpoints 8 0 and 0 One endpoint of the minor asis 35 Findr Draw a picture with the given information to help you get started File submissions Files You can drag and dupfestere at

2 Determine h x given that h x 12x 14x 10 and h 1 8

5 2 Determine f x given that f x 12x 30x and 4 23

tan xoi tanx Secx

Consider the following table a Use this data and a left endpoint Riemann sum to estimate the integral 20 f x dx b Use this data and a right endpoint Riemann sum to estimate the integral 20 f x dx 140 T 04812 f z 53 52 49 43

Evaluate the following integral by interpreting it in terms of areas from drawing the graph of the function being integrated 5 x dx

Evaluate the integral of the function graphed using the formula for areas of triangles and circles and subtracting the areas below the x axis

A solid is formed between f x and the x axis so each slice perpendicular to the x axis is a right triangle whose base height Represent the volume of this solid as a definite integral Volume b dx a y f x each slice is a right triangle with base Height b X

In the following exercises find each indefinite integral using appropriate substitutions dx 9 x 397 398 399 J dx 1 16x 400 dx 9 x dx 25 16x

O Name a pair of angles that are a linear pair D E F C A OA ZAFE and ZCFD OB ZAFC and ZEFD OC ZAEF and ZDEF OD ZAFE and ZAFC B Choose the correct answer below

In a certain base 5 numeration system the colors shown here are used instead of numerals Subtract the given numbers in the indicated base Choose the correct answer below G Y R 5 R G5 OA ORB OB ORIG O C R 5 5 SO D OBG 305 B 0 R 1 2 G 3 Y 4

1 Listen Integrate dx x ln x ln x 1 sec ln x c Osec In x c 1 O sec ln x c Ocsc In x c

1 Listen Evaluate f O 0 10 6 0 1 10 I 3 dx 16

Determine the integral e e x dx O ee c Oeet c Oe c Oe c

Determine lim O 1 8 8 01 cos x sin z 1

Listen Integrate f Otan x c O 3 64 Otan x c tan x c dx 9x 16 16 12 tan x c

Integrate f O VE 2x 4x 6 tan c O 2 V 4 tan 2 1 c 4 dx hint complete the square on the denominator 2 tan 2 1 x 1 2 Otan c c

Determine lim x e x x0 O 1 01 O o O O

Integrate f sin x cos x dx sin x 1 e 1 cos x e 1 e 1 sin x e 1 e 1 sin x e c c c c

Listen Integrate fx5 2 dx O 5 1 2 ln 5 O 5 2 In 5 5 22 2 ln 5 5 2 In 5 c c c c

The equivalent Hindu Arabic numeral is 222 What is the equivalent Babylonian numeral Choose the correct answer below O A III O B VI OC TVY O D WI

The average rate of change between two points is equivalent to O The slope of the tangent line at the second point O The slope of the tangent line between the points The slope of the tangent line at the first point O The slope of the secant line between the points O The slope of the secant line at the first point

5 4g x dx 7 3g x 8 dx 6 5dx 25 god Lac 8 3f x 2g x dx

Sketch the region enclosed by the curves and find its area a b c d 1 y x y x x x 1 y x 4x y 0 x 0 and x 2 y x y x 2 y x y x 2

7 Find the area of the region bounded by the graph of y x 1 the x axis and the vertical lines x 0 and x 1 3pts

3x x 5 x 12x 5x 2x 1 5 pts Evaluate the limit lim Lim 3x X s X 12x 5X 2X WA

Add a term to the expression to complete the square 2 7171 a Add a term to the expression to complete the square Make it a perfect square 1 t Type an integer or a simplified fraction

1 F 81 Select the correct choice below and if necessary fill in the answer box to complete your choic O A 1 81 OB The square root is not a real number

Determine whether the 8 5 Is the statement true or false 00 O True False

by using appropriate substitutions In x 328 329 330 331 332 333 334 S S l n Sta S 336 337 338 d x x lnx X s dx x ln x 1 dx dx x ln x ln lnx tan 0 de x 1 COS X rsinx xe ln sin x tan x 335 In cosa tan ada Je X COS X x dx 2 x e da dx dx sin x cos xdx

76 7 14 3 27 3 Graph of y f x A graph of f x is shown The numbers shown represent the geometric area of each region Evaluate the following definite integrals a 2 f f z dz help numbers b 2 Jo Jawa 3 c ff x dx C 0 2 d 3f x dx

In x27 X dx x 0 Hint Use the properties of logarithms inx dx Type an exact answer Use parentheses to clearly denote the argument of each function

Find the most general antiderivative of the function f 2 4 3 Use an upper case C for any arbitrary constam F x 4

Evaluate Be sure to check by differentiating 4 3 1 8 6x dx x 1 dx 8 6x Type an exact answer Use parentheses to clearly denote the argument of each functio

Find the volume of the solid formed by rotating the region enclosed by about the x axis 2 0 x 1 y 0 g 8 r

and the most general antiderivative of the function f x 6e 3 sec x Use an upper case C for any arbitrary constants F x

The functions f x x 1 and g x 2 2 are graphed below 5 4 f x It cannot be determined 2 g x B 2 C 46 Which statement is true about the average rate of change between two function from x 1 to x 0 f x has a greater average rate of change than g x Ax has a smaller average rate of change than g x f x and g x have the same average rate of change

2 cos x 1 x sin 2x 1 x TT log 1 e dx

If h a h b then what is the value of g h z h x dz

Express the integral as a limit of Riemann sums Do not evaluate the limit Use the right endpoints of each subinterval a your sample points lim 1 5 1 1 x 4 In x dx