BC Integral Jeopardy

Basic Integrals

100

int(x+1)dx

x²/2+x+C

200

int(cos3x)dx

sin(3x)/3 +C

300

int(e^(4x))dx

e^4x/4+C

400

int(sqrtx+1/x-2)dx

2/3x^(3/2)+lnx-2x+C

500

int(4sec(8x)tan(8x)dx

1/2sec(8x)+C

Fundamental Theorem

100

d/dxint_0^xt^2dt

x²

200

d/dxint_x^17lnqdq

-lnx

300

d/dxint_-2^(x^3)sintdt

3x²sin(x³)

400

d/dxint_x^(3x)sqrttdt

3sqrt(3x)-sqrt(x)

500

d/dxint_(e^x)^(sinx)udu

cosxsinx-e^xe^x

U-substitution

100

int(xsin(x^2))dx

-1/2cos(x²)+C

200

int(x^2(x^3+7)^5)dx

1/18(x^3+7)^6+C

300

int((lnx)^6/x)dx

1/7(lnx)^7+C

400

int(2x^3sin^4(x^4)cos(x^4)dx

1/10sin⁵(x⁴)+C

500

int(xcot(x^2)csc^3(x^2))dx

-1/6csc^3(x^2)+C

Definite Integrals

100

int_0^1xdx

1/2

200

int_2^5e^(2x)dx

1/2e^10-1/2e^4

300

int_0^9(sqrtx+1)dx

27

400

int_2^4(4/x+x)dx

4ln4+8-4ln2-2   OR 4ln4-4ln2+6

500

Find the average value of x^2+6 on the interval [0, 3]

9