Calculus Review

Antiderivatives

100

dy/dx = -9/x^4

y = 3/x^3 + C

200

FREE POINTS

BONUS 200 POINTS

300

dy/dt = 3t^2

y = t^3 + C

400

dy/dx = x^3/2

y = 2/5x^5/2 + C

500

dy/dx = 1/(x(x^1/2)) Rewrite: Integrate: Simplify: Show all steps.

y = -2/x^1/2

Indefinite Integrals

100

∫ (x+3)dx

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

200

∫ x^2/3 dx

3/5x^5/3 + C

300

∫ (2sinx + 3cosx)dx

-2cosx + 3sinx + C

400

∫ (1 - cscxcotx)dx

x + cscx + C

500

∫ (x^2 + x + 1) / (x^1/2)dx

2/5x^5/2 + 2/3x^3/2 + 2x^1/2 + C

Inverse Trig

100

Solve. arcsin(-1/2)

-π/6

200

∫1/(16+x^2)dx

1/4arctan(x/4) + C

300

∫ 1/(1-(x+1)^2)dx

arcsin(x+1) + C

400

Solve. arctan(3^1/2)

π/3

500

Differentiate. y = arcsin3x / x

Write on board.