6-6 Applying Properties of Definite Integrals

6-6 Applying Properties of Definite Integrals

Guided Notes

Multiple Choice

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

• antiderivative

• indefinite integral

• definite integral

• derivative

Multiple Choice

The fundamental theorem of calculus is basically:

• calculating the area under a curve

•  $\int_a^b\ f\left(x\right)\ dx=F\left(b\right)-F\left(a\right)$ 

• integrating a function, with no +C

• using rectangles to approximate the area under a curve

• we didn't learn this!

Multiple Choice

Which of the following is incorrect?

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

•  $\int_a^af\left(x\right)\ dx=0$  

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

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

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

Multiple Select

The area under a curve can be represented by  $\int_a^bf\left(x\right)\ dx$  only if:

*Choose all correct answers

•  $f\left(x\right)$  is positive

•  $f\left(x\right)$  is continuous

•  $f\left(a\right)$  exists

•  $f\left(b\right)$  exists

Multiple Choice

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

• positive

• negative

• zero

Multiple Choice

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

• positive

• negative

• zero

Multiple Choice

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

• positive

• negative

• zero