1. ## cal 2

evaluate the definite intergral with limits squar root of pi and 0 xsin(x^2)dx. give answer in decimal number with four places.

"" limits 5 and 1 1/square root 2x-1 dx give answer in decimal number with four places.

"" limits 2 and 0 x/square root 1+2x^2 dx.""

2. Originally Posted by lay137
evaluate the definite intergral with limits squar root of pi and 0 xsin(x^2)dx. give answer in decimal number with four places.
Do you know the fundamental theorem of calculus?

Do you recognise what $\displaystyle x \sin(x^2)$ is the derivative of?

Hint: consider $\displaystyle \frac{d}{dx} \cos(x^2)$.

RonL

3. Hello, lay137!

These are all straight Substitution problems . . .

[int] x·sin(x²) dx . . . from 0 to √2
Let: u = x²

[int] dx / √(2x - 1) . . . from 1 to 5
We have: .[int] (2x - 1)^(-½) dx

Let: u = 2x - 1

[int] x dx / √(1 + 2x²) . . . from 0 to 2
We have: .[int] (1 + 2x²)^(-½) (x dx)

Let: u = 1 + 2x²