Indefinite and definite integrals and U-substitution

• ln(2x²+6) + C
• ln(2x²+6)(4x) + C
• 1/(2x²+6) + C
• 1/(2x²+6)² + C

• e/2
• 1/2
• 1/2(ln(5)-ln(3))
• 0

• -½x^-2 + C
• -⅖x^-5/2 + C
• 2x^1/2 + C
• -2x^-1/2 + C

Tags

CCSS.7.EE.A.1

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

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

• positive

• negative

• zero

Find the average value of the function  $f\left(x\right)=x+3$  on the interval  $\left[3,9\right]$  

•  $54$  

•  $67.5$  

•  $7.5$  

•  $9$  

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

•  $\int_{-1}^2f\left(x\right)\ dx$  

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

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

•  $\int_{-2}^1f\left(x\right)\ dx$  

The shaded area shown in the figure can be represented by which of the following integral expressions?

•  $\int_0^3f\left(x\right)\ dx$  

•  $-\int_0^1f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$  

•  $\int_0^1f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$  

•  $\int_1^0f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$  

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!