Antiderivatives and Slope Fields

∫(4 - 18x)dx

• F(x) = -18
• F(x) = 4x - 9x²
• F(x) = 4x - 9x² + C
• F(x) = (4 - 18x)² /2 + C

∫ t⁶ dt

• 6t⁵
• 6t⁵ + C
• 1/7 t⁷ + C
• t⁷ + C

Tags

CCSS.HSA.APR.A.1

∫ - sinx dx

• -cos x + C
• cos x + C
• tan x + C
• 1/√1- x²

∫ 4 dx

• 0
• 4t + C
• 4x + C
• 2x² + C

Tags

CCSS.HSF.IF.A.2

∫ x(x² - 4) dx

• x²/2(x³/3 - 4x) + C
• .25x⁴ -2x² + C
• 3x²- 4 + C
• x⁴ - 4x² + C

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.B.3

∫25sec²x dx

• 25 secx tanx + C
• 25 tanx + C
• -25 tanx + C
• -25 sec x + C

Given v(t) = x^-9, find the general equation for the antiderivative.

• (1/8)x^-8 + C
• (-1/8)x^-8 + C
• (1/10)x¹⁰
• (-1/8)x^-8

∫ x(x² - 4) dx

• x²/2(x³/3 - 4x) + C
• .25x⁴ -2x² + C
• 3x²- 4 + C
• x⁴ - 4x² + C

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

If f'(x) = 4x and f(1) = 6, then f(2) =

• 6

• 8

• 9

• 12

Tags

CCSS.HSF.IF.A.2

Given G'(x) = x + 2 and G(0) = 3, find G(x).

• 1/2 x² + 2x + 3

• 1/2 x² + 2x + 6

• x² + 3

• x² + 2x + 6