Integrals Review

• Intermediate Value Theorem
• Rolle's Theorem
• Average Rate of Change
• Average Value of f

Tags

CCSS.HSF.IF.B.6

 $\int_{a\ }^{b\ }f\left(x\right)dx\ =?$  

• -2

• 2

• 10

• -6

• -cos(x⁶)
• sin(x⁶)
• 2x sin(x³)
• 2x sin(x⁶)

 $\int_0^3\left(x^2-2x-2\right)dx$  

• -6

• -16

• 1

• 2

 $\frac{\text{d}}{\text{d}x}\left(\int_{-1}^x\sin\left(t\right)dt\right)$  

•  $0$  

•  $\sin x$  

•  $\sin x+C$  

•  $-\sin x$  

 $\frac{\text{d}}{\text{d}x}\left(\int_x^1\sin\left(t\right)dt\right)$  

•  $0$  

•  $\sin x$  

•  $\sin x+C$  

•  $-\sin x$  

 $\frac{\text{d}}{\text{d}x}\left(\int_{-1}^1f\left(t\right)dt\right)$  

•  $0$  

•  $\sin x$  

•  $\sin x+C$  

•  $-\sin x$  

 $\int_{-1}^1\sin\left(t\right)dt=$  Hint:  think about the graph of sin(x)

•  $0$  

•  $\pi$  

•  $\sin x+C$  

•  $-\sin x$  

• Average Rate of Change
• Average Value of f
• Intermediate Value Theorem
• Rolle's Theorem

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.6

Evaluate: (Hint, make a graph.)

• 40

• 20

• 10

• Not possible