Calculus Antiderivatives Intro

Given v'(x) = -sinx, determine the general form of the antiderivative.

• v(x) = cosx

• v(x) = -cosx

• v(x) = -cosx + C

• v(x) = cosx + C

Find the general form of the antiderivative of

x²

• (1/3)x³ + C

• 3x³ + C

• (1/3)x³

• 2x

Find the general form of the antiderivative of

4x - 7

• 4 + C

• 2x² - 7x + C

• (1/2)x² - 7x + C

• 8x² + C

What is an antiderivative?

• the opposite of a derivative

• the same as a derivative

• a second derivative

• it always represents velocity

What does C represent in an antiderivative?

• a variable

• a constant

• none of these

• both a variable and a constant

Find the general antiderivative:

x²(x + 6)

• (1/4)x⁴ + 2x³ + C

• (x²/2)(x³/3 + 6x) + C

• 3x² + 12x + C

• x⁴ + 6x³ + C

Find the specific antiderivative of

f'(x) = 8x³ + 12x if f(1) = 10

• f(x) = 2x⁴ + 6x² + 10

• f(x) = 2x⁴ + 6x² + 2

• f(x) = 4x² + 12x - 6

• f(x) = 24x² + 12x - 26

Find the specific antiderivative of

f"(x) = 40x³ + 20

if f(1) = 0 and f'(1) = 38.

• f(x) = 40x³ + 10x² + 38x + 1

• f(x) = 40x³ + 10x² - 102x + 52

• f(x) = 2x⁵ + 10x² + 8x - 20

• f(x) = 2x⁵ + 10x² + 38x + 1

∫(4 - 18x)dx

• -18

• 4x - 9x²

• 4x - 9x² + C

• (4 - 18x)² /2 + C

∫ 4 dx

• 0

• 4t + C

• 4x + C

• 2x² + C