Integration Jeapordy

Indefinite Integrals

100

What is the integral of x²+4

1/3(x³)+4x+C

200

Integrate the function 2/x

2ln|x|+C

300

What is the antiderivative of 5x²-8+1/2x

(5/3)x³-8x+(1/2)ln|x|+C

400

Find the integral of e^3x+2

(1/3)e^3x+2+C

500

Integrate the function 5√2x+3

5/3(2x+3)^3/2+C

Indefinite Integrals Using Substitution

100

Integrate the function (2x+5)³

1/8(2x+5)⁴+C

200

What is the integral of the function 1/(1-6t)³

1/18(1-6t)³+C

300

Integrate the function (sinx)(cosx)

1/2sin²x+C or -1/2cos²x+C

400

What is the antiderivative of 3x²(x³+1)⁶

((x³+1)⁷)/7) +C

500

The integral of x²/√(1-x)

(-2/15)√(1-x)(3x²+ 4x +8)+C

Indefinite Integrals With Trigonometry

100

What is the integral of 2sinx

-2cos(x)+C

200

What is the integral of 3sinx+1/2cosπx

-3cosx+(1/2π)sin(πx)+C

300

What is the antiderivative of sin4x

(-1/4)cos(4x)+C

400

Integrate the function cos²(x)+sin(x)

(1/2)x+(1/4)sin(2x)-cos(x)+C

500

What is the antiderivative of 3cos²xsinx

(-2/3)cos³x+C

Definite Integrals With One Curve

100

The area under the curve of y=x+3 from x=0 to x=4

20

200

The area under the curve of f(x)=2x²+4 fromx=2 to x=5

90

300

The area under the curve of the function 

7/(5x+2) from x=0 to x=6

(28ln|2|)/5 or about 3.88

400

Find the area under the curve of f(x)=e^(4x+3) from x=0 to x=2

(e¹¹/4)-(e³/4) or about 14963.5

500

Find the area under the curve of f(t)=t²sin(2t) from x=0 tp x=2π

-2π²

Definite Integrals With Two Curves

100

Find the area between the curves of y=x² and y=2x+3

-32/3

200

Find the area between the curves of y=x²+2 and y=3x³ from x=0 to x=3

-183/4

300

Determine the region bounded by the equations y=x²+4 and y=sin(x) from x=-1 to x=2

14.04

400

Find the area between the curves of y=4/(5x+3) and y=(x-3)²+5 from x=[1,5]

(12ln|7/2|+220)/15 or about 18.1

500

What is the area of the region bounded by the equation y=(sin²x)(cosx) and y=4sinx-2 from x=0 to x=π

8-2π