Chapter 24 Review

Polynomials

100

Integrate ∫(3x²)dx

What is x³+C

200

Integrate and simplify ∫(4x⁵-4x)dx

What is (2/3)x^6 - 2x²+C

300

Integrate ∫x*sqrt(x)dx

What is (2/5)x^5/2 +C

400

Find f(x) if f`(x) = x³-3 and f(2) = 1

What is f(x)=(1/4)x⁴-3x+3

500

Integrate ∫(6x⁵+4x³)(5x⁶+5x⁴)³ dx

What is (1/20)(5x⁶+5x⁴)⁴ + C

Mixed Exponentials and Trig 1

100

Integrate ∫e^x dx 

What is e^x+C

200

Integrate ∫2e^2x+2 dx 

What is e^2x + 2x + C

300

Integrate ∫(2x+2)e^{x^2+2x} dx 

What is e^{x^2+2x}+C

400

Find f(x) if f'(x) = 8e^4x and f(0) = 5

What is f(x) = 2e^4x + 3

500

Integrate ∫ sin²(4x) dx

What is (x/2)-(1/16)sin(8x)+C

Mixed Exponentials and Trig 2

100

Integrate ∫cos(3x-pi) dx

what is (1/3)sin(3x-pi)+C

200

∫ e^-x (cos x -sin x) dx 

hint: consider the derivative of e^-xsin x

what is e^-xsinx + C

300

Integrate ∫[ sin³x cosx]dx

What is (1/4)(sinx)^4+C

400

Integrate ∫ sin⁵(x)cos³(x) dx

what is (1/6)sin⁶x - (1/8)sin⁸x + C

500

find f(x) if

 f''(x) = sec³x sin x dx 

 f'(0) = (1/2), and f(0) = 2

What is (1/2)tan x + 2

Definite Integrals

100

evaluate ∫ (x²+3x) dx on [1, 3]

What is 62/3

200

evaluate ∫cos(x/2)dx on [0,pi]

What is 2

300

evaluate ∫(secx)^2dx on [-pi/4,pi/4]

What is 2

400

evaluate  ∫ xe^{-2x^2} dx on [1,2]

What is 1.557

500

evaluate ∫ sin²(x/2) dx on [0, pi/6]

what is pi/12 - 1/4