Intro to Integration Review

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

• your aunt derivative

• indefinite integral

• definite integral

• derivative

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!

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  $\int_1^3\left(x-2\right)\ dx$  is:

• positive

• negative

• zero

Tags

CCSS.HSA.SSE.A.1

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

• positive

• negative

• zero

Integrate  $\sqrt{x}$  with respect to x

•  $x^{\frac{1}{2}}+c$  

•  $\frac{1}{2}x^{-\frac{1}{2}}+\ c$  

•  $\frac{2}{3}x^{\frac{3}{2}}+\ c$  

•  $\frac{3}{2}x^{\frac{3}{2}}+\ c$  

Tags

CCSS.HSN.RN.A.2

 $\int8x^{-3}dx$  

•  $-2x^{-4}+C$  

•  $4x^{-3}+C$  

•  $\frac{8}{-3}x^{-2}$  

•  $-4x^{-2}+C$  

Tags

CCSS.7.EE.A.1

 $\int\left(x^{-1}-1\right)dx$  

•  $\ln\left|x\right|-x+C$  

•  $\frac{x^{-2}}{-2}-x+C$  

•  $\ln\left|x\right|-1+C$  

•  $1-x+C$  

Integrate $\int_{ }^{ }\sin x\ dx$  

•  $=\tan x+c$  

•  $=-\cos x+c$  

•  $=-\sec x+c$  

•  $=\operatorname{cosec}\ x\ +c$  

If  $\int_1^3\ f\left(x\right)\ dx\ =5,\ \int_1^{11}\ f\left(x\right)\ dx=24$  and  $\int_1^3\ g\left(x\right)\ dx=7,$  evaluate  $\int_3^{11}\ f\left(x\right)\ dx$  

•  $-19$  

•  $41$  

•  $-11$  

•  $19$