MAT152 Calculus II Test 1
Prof. Porter
NAME:_______________________
Show all work for full credit.
After performing a quadratic regression on the data above, you obtain the formula y(x)=  x 2  2 x  10 . Use
this to solve the following three questions.
1. Find the area under the curve y(x) above the x- axis and between x = 0 and x = 4 by estimating the area
with 4 rectangles of equal width.
Draw a picture of your approximation.
2. Set up the integral and use the Fundamental Theorem of Calculus to find the exact answer.
3. What is the average value of the function over the interval [0,4]
For problems 6-10 use the following:
Suppose a V- shaped Vase is found to be modeled by taking the following equations and rotating them about
the y-axis and cutting at the line y = 10 and using only the parts above the x-axis.
y  x / 10 and y  x
4. Draw a picture of the vase:
To get the area of a slice of the vase, find the area between the curves y  x / 10 and y  x when above
the x-axis and y<10.
5. Use the Washer Method to find the amount of material required to make vase.
6. Set up the integral for the Shell Method that could be used to find the volume of the inside of the
vase.(HINT: use only the inside function)
If you are confronted with the below integrals, how would you evaluate them? Give a result.
sin(ln( 2 x))
7.
 x dx
3
 x sinh( x
8.
2
)dx
0
9. Evaluate the integral by using the table of integrals.
3

9  x 2 dx
0
Confirm by using a geometric approach. Draw the picture.
Confirm with a calculator.
10. Evaluate the integral:  cosh 4 (sin( x)) sinh(sin( x)) cos( x)dx
11. Evaluate:
x 1
 ( x  3)( x  2) dx
12. Evaluate   3 sin  d
13. Evaluate:  cos3 x sin 2 xdx
14. Given the following evaluation of the integral using trig substitution:
1
 16  x2 dx