U-Substitution and Riemann Sub

∫ 2x cos(x²) dx

• sin(x²) + C

• 2 sin ( 2x ) + C

• (1/2) sin(x²) + C

• 4 cos(2x ) + C

Use the indicated substitution to evaluate the integral.

 $\int7x^6\left(x^7+1\right)^8dx\ ,\ \ \ u\ =\ x^7+1$  

•  $\frac{\left(x^7-1\right)^9}{9}+c$  

•  $\frac{\left(x^7+1\right)^9}{9}+c$  

•  $\frac{\left(x^7+1\right)^8}{8}+c$  

•  $\frac{\left(7x^6+1\right)^9}{9}+c$  

Use substitution to evaluate the integral $\int\frac{2x}{\left(x^2+3\right)^3}\ dx$  

•  $-\frac{1}{2\left(x^2+3\right)^2}+C$  

•  $-\frac{3}{2\left(x^2+3\right)^2}+C$  

•  $-\frac{5}{2\left(x^2+3\right)^2}+C$  

•  $-\frac{1}{\left(x^2+3\right)^4}+C$  

What kind of Riemann sum is described by the diagram?

• Left-hand

• Right-hand

• Midpoint

Approximate the area under y=h(x) from x=-2 to x=4 using a Right-hand sum and three equal subdivision

• 20 units²

• 26.5 units²

• 28 units²

How would you describe the Reimann Sum shown in the picture?

• overestimation

• underestimation

• real area

Find the right-hand Riemann Sum, with three sub-intervals indicated by the table.

• 28

• 16

• 34

• 23

Find the Left-hand Riemann Sum, with three sub-intervals indicated by the table.

• 28

• 16

• 34

• 23

Use a trapezoidal sum with four intervals from the table to estimate the integral of 0 to 9 of V(t).

• 128/2

• 134/2

• 186/2

• 151/2

What should be assigned to u in the integral?

• 2x²

• sin (2x²)

• 5x

• no u needed

Tags

CCSS.HSF-BF.B.4A