AP Calculus 5.3 Review

The area under a curve is calculated using which mathematical concept?

• antiderivative

• indefinite integral

• definite integral

• derivative

The result of  $\int_1^3\left(x-2\right)\ dx$  is:

• positive

• negative

• zero

Tags

CCSS.HSA.SSE.A.1

The result of  $\int_0^2\left(x^2-2x+1\right)\ dx$  is:

• positive

• negative

• zero

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

The result of  $\int_0^2\left(x^3-2x^2-x+1\right)\ dx$  is:

• positive

• negative

• zero

The shaded area in the figure is represented by which of the following integral expressions?

•  $\int_{-1}^2f\left(x\right)\ dx$  

•  $-\int_2^{-1}f\left(x\right)\ dx$  

•  $-\int_{-1}^2f\left(x\right)\ dx$  

•  $\int_{-2}^1f\left(x\right)\ dx$  

Which of the following is incorrect?

•  $\int_b^af\left(x\right)\ dx=-\int_a^bf\left(x\right)\ dx$  

•  $\int_a^af\left(x\right)\ dx=0$  

•  $\int_a^bf\left(x\right)\ dx+\int_b^cf\left(x\right)\ dx$  
   $=\int_a^cf\left(x\right)\ dx$  
  

•  $\int_a^bf\left(x\right)\ dx-\int_b^cg\left(x\right)\ dx$  
   $=\int_a^c\left(f\left(x\right)-g\left(x\right)\right)\ dx$  
  

•  $\int_a^bf\left(x\right)\ dx-\int_a^bg\left(x\right)\ dx$  
   $=\int_a^b\left(f\left(x\right)-g\left(x\right)\right)\ dx$  
  

Tags

CCSS.HSA.SSE.B.3

• 2
• 4
• 1
• Not possible

• -8
• 8
• -2
• 2

Given the following integral values, find the integral below

• A

• B

• C

• D

Given the following integral values, find the integral below

• A

• B

• C

• D