Application of Integrals

Question 1

Anti derivative of indefinite integral

Answer 1

1/(n+1)*x^(n+1) +c

Question 2

Steps in solving u substitution

Answer 2

1. U=g(x) du=g’(x)d
2. Find the anti derivative of f(u), F(u)
3. Substitute u=g(x)
4. Check

Question 3

Derivative of tan(x) and derivative of sec(x)

Answer 3

Sec^2(x) for tan(x)

Sec(x)tan(x) for sec(x)

Question 4

Solving Dynamic Motion with Integration

Answer 4

Xend=Xstart+INtegral(v(t)dt) t=0, now.

Question 5

Integration by Parts

Answer 5

Integral(udv)=uv-integral(vdu)

Question 6

Partial Fractions

Answer 6

Split up the bottom of the fraction into two factors, and then write A/(one factor)+B/(another factor). Then solve for A and B and then integrate it. This can only work if the numerator is a lower order then the denominator.

Question 7

Solving improper integrals

Answer 7

That is when integrals are from -infinity to infinity. Split it up into to integrals. ONe integral from -infinity to zero and the other from 0 to positive infinity.