CALCULUS Integration & other topics

What is an antiderivative?

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

∫(3x⁴+2)⁴(12x³)dx

• ½(3x⁴+2)⁴+C
• (3x⁴+2)⁴+C
• ⅕(3x⁴+2)⁵+C
• ⅓(3x⁴+2)⁶+C

∫ 2 x (x²- 3)^(1/2) dx

• (x²- 3)^(3/2)+C

• (3/2)(x²- 3)^(3/2)+C

• (2/3)(x²- 3)^(3/2)+C

• (2/3)(x²- 3)^(-1/2)+C

∫ 6 x (x² +1 )² dx

• ( x² + 1)³ + C

• 3 ( x² + 1)³ + C

• ( x² + 1)¹ + C

• 6 ( x² + 1)³ + C

∫ x (x² + 7 )^(1/3) dx

• (3/4) ( x²+ 7 )^(4/3) + C

• (3/8) ( x²+ 7 )^(4/3) + C

• ( x²+ 7 )^(4/3) + C

• (3/2) ( x²+ 7 )^(4/3) + C

∫ (2 - x)⁵ dx

• -5 (2 - x )⁴ + C

• ( 2 - x )⁶ + C

• (1/6) ( 2 - x )⁶ + C

• -(1/6) ( 2 - x )⁶ + C

Find the integral:

• 1/3(x⁴ + 3)³ + c

• 1/12(x⁴ + 3)³ + c

• 3/4(x⁴ + 3)³ + c

• 1/4(x⁴ + 3)³ + c

Find the integral:

• 1/8(4x² + 3)⁴ + c

• 1/2(4x² + 3)⁴ + c

• 1/32(4x² + 3)⁴ + c

• 1/4(4x² + 3)⁴ + c

Find the integral:

• -1/3 (16 - x³)^-1 + c

• 1/3 (16 - x³)^-1 + c

• - (16 - x³)^-1 + c

• -1/2 (16 - x³)^-2 + c

Find the integral:

• 1/3 (x³ + 2)^3/2 + c

• 1/2 (x³ + 2)^-1/2 + c

• 2/3 (x³ + 2)^3/2 + c

• 2/9 (x³ + 2)^3/2 + c