Calculus Antiderivatives

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

∫ - sinx dx

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

∫(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

∫ x(x² - 4) dx

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

∫25sec²x dx

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

∫sec²x dx =

• -cotx + C
• cotx + C
• -tanx + C
• tanx + C

What is an antiderivative?

• The opposite of a derivative
• The same as a derivative
• A second derivative
• It always represents velocity.

Integration is...

• ...the finding of an integral or integrals

• ...somehing I've learnt in Tadika

• ...a differentiation of x^2 to become 2x

• ...an antiderivative