Integration

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
• Unknown

∫(4 - 18x)dx

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

∫(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

• = 0