## Star 5 years ago integrate x(3+x^2)^1/2 between limits of 1 and 0 (x times square root of 3 plus x squared)

1. anonymous

$\int\limits_{0}^{1} x \sqrt{3+x^2} dx$

2. anonymous

right?

3. star

yes! :)

4. star

i've tried by parts and got 8/3 for first bit but not sure how to work out the second bit

5. anonymous

$(1/2) \int\limits_{o}^{1} (2x)(x+x^2)^{1/2} dx$

6. anonymous

oho there is 3 inplace of first x :)

7. anonymous

$2/3 [(3+x^2)^{3/2}]$

8. anonymous

now u can put the limits

9. anonymous

(2/3)(3+1)^(3/2)

10. anonymous

(2/3)[(3+1)^(3/2)-(3)^(3/2)]

11. star

the answer is supposed to be $8/3 - \sqrt{3}$

12. star

but i can't get that answer after i put the limits in

13. anonymous

(2/3)[8-3sqrt(3)]

14. anonymous

15. anonymous

is it wrong?

16. anonymous

$\int\limits _0^1x \sqrt{\left(3+x^2\right)}dx = \frac{8}{3}-\sqrt{3}$