Integral Calculus Answers

Let G be the region enclosed by the curves y=4/x and y=5-x
Find the volume of the solid generated by rotating the region G about the x-axis.

1. Complete the perect square and use tables of integration to integrate
∫ [(1) / ( sqrt(x^(2) - 3x + 6) )] dx

2. Use a substitution technique and then the table of integration to integrate

∫ (x^5)(sqrt(x^(4) - 4)) dx

Given: x^5 = (x^3)(x^2)

Sketch the area between the curve y = (x-4)^2 and the line y = 2x+7. Use a definite integral to find the area between these two curves.

Find the indefinite integral

∫‍ (x)/sqrt(3-x) dx

Evaluate the definite integrals listed below

a. ∫ (e,6) (ln(x))/x dx

b. ∫ (-1,0) x/(x + 2) dx

c. ∫ (0,3) xe^(2x^2) dx

with the first bracketed number being on the bottom of the integral symbol and the second being on the top

Describe the area represented by the definite integral ∫ (0,3) 2x^3 dx

Find each indefinite integral

a. ∫ e^x(e^(3x)-5) dx

b. ∫ x(sqrt(2x^2+3) dx

c. ∫ (x)/(sqrt(3-x)) dx

Find the surface area of the band of the sphere generated by revolving the arc of the circle
x2+y2=r2
lying above the interval [-a,a],a,r

Find
∫e^1/3dx

3e^x/3+c
ex+c
3e1/3+c
1/3ex+c

∫xcosax^2dx
with respect to x

cos^3x+c
sin2x+c
sec^2x+1
1/2asinax^2+c