Antiderivatives

Given v(t) = -sin(2x), determine the general for the antiderivative.

• cos(2x)
• 2cos(2x)
• -cos(2x)
• 1/2cos(2x)

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

∫(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

∫ 3e^x dx

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

Tags

CCSS.HSF.IF.C.8

∫ 4 dx

• 0
• 4t + C
• 4x + C
• 2x² + C

∫(4/x - e^x ) dx

• 4ln x - e^x
• 4 ln x + e^x + C
• 4 ln x - e^x + C
• 4/x²  - 4e^x + C

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSF.BF.B.5

∫ 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

∫-csc²x dx

• cscx + C
• cotx + C
• secx + C
• tanx + C