Finding the Area Between Curves and Definite Integral

Name
Institution affiliation
Course
Date
Question 1
-212x2+5 dx
-212x2+5 dx
-21 (2x2+5)dx
6+15
21
Question 3
-31x3+1 dx
-31( -x3-1)dx + -11( x3+1)dx
18+-11( x3+1)dx
18+2=20
Question 5
-212x-(x2-3) dx
Eliminating absolutes, we get:
-21( x2-2x-3)dx + -11(2x-( x2-3))dx
73+-11(2x-( x2-3))dx
=73+163
=233
Question 7
x^2-30=10-3x
x=5, x=-8
-85/x2-40+3x/ dx
Eliminating absolutes
-85(-x2-3x+40) dx
-637/3+117/2+520=2197/6
Question 9
Finding the intersection
x2=2x
x2-2x=0
x=0 or 2
02|x2-2x|dx
Eliminating absolutes, we get:
02(-x2+2x) dx
-02(-x2)dx+ 02(2x)dx
02(x2)dx= 83
02(2x)dx =4
* 83+ 4
=43
Question 11
161x+12 dx
12(1x-12)dx+ 26(-1x+12)dx
ln2- 12-ln6+ln 2=ln23+ 32
Question 13
-11/ex-3-ex/dx
Eliminating absolutes
=-1ln3/2-2ex+3dx+ln3/21(ex-(3-ex))dx
3ln(3/2)+2/e+2e+3ln(3/2)-6
=6ln(3/2)+2e+2/e-6
Question 42
b)1/2*3(2+1)
6/2=3
Question 43
4 rectangles
Rectangle 1= 1*3=4
Rectangle 2=1*5
Rectangle 3=1*7