Basic 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

• -(24/4)x⁴+C
• -4x⁶+C
• -4x⁵+C
• -24x⁶+C

• -3x+C
• 0
• -3x
• -1/3x+C

• -1/x⁴+C
• -x⁴+C
• x^-4+C
• -4/x⁴+C

Tags

CCSS.7.EE.A.1

 $\int_1^9\sqrt{x}dx$  

• 52/3

• 18

• 1/3

• 39

• none of these

What is the area between the function  $f\left(x\right)=\left(2x-2\right)^2$  and the x-axis from -1 to 1?

• 16

• 16.3333

• 32/3

• none of these

What is the average value of  $f\left(x\right)=\frac{4}{x^2}$   from 1 to 4?

• 3

• 1

• 1.155

• none of these

What is  $2\int_{-1}^6\ g\left(x\right)dx$  

• 11

• 5.5

• -10.5

• none of these

When do you need to use + C?

• Definite Integrals (includes limits of integration)

• Indefinite Integrals (does not have limits of integration)