Calculus Answers

Evaluate the limits. Applying L'Hopital's Rule Yield
lim┬(x→0)⁡〖1/x^3 〗 ∫_0^x▒〖t^2/(t^4+1) dt〗

Find a function f (x) and a number k such that
3 + ∫_k^x▒〖f(t)dt=e^5x 〗

Use cylindrical shells to find the volume of the solid that results when the region enclosed by x = y^2 and x = y is revolved about the line y= -1

Find the area of the region enclosed by x = y^2 - 4y + 2 and x = y-2

Find the arc length of the curve x= y^4/8+1/〖4y〗^2 from y=1 and y=4

Evaluate the integral
∫▒√(〖1+x〗^(-2/3) ) dx
using the substitution u=1+x^(-2/3) dx

Evaluate the limits:
lim┬(x→0)⁡〖1/x^3 〗 ∫_0^x▒〖t^2/(t^4+1) dt〗

Use an appropriate local linear approximation to estimate the value of (122)^2/3

Integral Calculus
1. ∫ x^4-2x^3+3x^2-x+3/x^3-2x^2+3x dx

1. ∫ lnx/(1+x^2) dx
2. ∫ sinx/cosx(1+cos^2x) dx