Friday

December 19, 2014

December 19, 2014

Posted by **John** on Thursday, March 7, 2013 at 12:03am.

- Calculus -
**Count Iblis**, Thursday, March 7, 2013 at 11:55amPut x = 3 sinh(t), then:

Integral from 0 to 4 of

x^3 sqrt{9+x^2} dx =

Integral from 0 to arcsinh(4) of

3^5 sinh^3(t) cosh^2(t) dt =

3^5 Integral from 0 to arcsinh(4) of

sinh(t) [cosh^2(t) - 1] cosh^2(t) dt =

3^5 Integral from 0 to arcsinh(4) of

[cosh^2(t) - 1] cosh^2(t) dcosh(t)

Putting cosh(t) = u gives:

3^5 Integral from 1 to sqrt(17) of

[u^2 - 1] u^2 du =

3^5 {sqrt(17)[1/5 17^2 - 1/3 17] + 2/15 }

You then need to round this off to below.

**Answer this Question**

**Related Questions**

Calculus - Given that \displaystyle \int_0^4 x^3\sqrt{9+x^2} dx = a, what is the...

Algebra - What is \left \lfloor ( 3 + \sqrt{5} ) ^3 \right \rfloor?

Calulus - Given \displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \...

Simple Calculus - Evaluate \displaystyle \lim_{x \to 0} \frac{\sqrt{2}x}{\sqrt{2...

Trigonometry - ABC is a non-degenerate triangle such that 2\sin \angle B \cdot \...

Math/Calculus - Solve the initial-value problem. Am I using the wrong value for ...

calculus - It is known that if m <= f(x) <= M for a <= x <= b, then ...

Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...

calculus - a. The value of \displaystyle \int_{-2}^{-1} \frac{14}{ 4 x } dx is b...

Calculus - Given f(x) = x^4 + 6x^3 - 15x + 7, evaluate \displaystyle \lim_{h \to...