Thursday

August 21, 2014

August 21, 2014

Posted by **Erica** on Tuesday, October 18, 2011 at 8:45pm.

∫ from 1 to 4 of (√x) (ln√x) dx

Im not really sure what to choose for u and dv.

Thank you so much for the help!!

- Calc -
**Steve**, Wednesday, October 19, 2011 at 5:32amTry to set u to something that gets simpler in the derivative.

u = ln √x

du = 1/√x * 1/2√x dx = dx/2x

dv = √x

v = 2/3 x^{3/2}

∫ u dv = uv - ∫v du

= 2/3 x^{3/2}ln √x - ∫ 1/3 √x dx

= 2/3 x^{3/2}ln √x - 2/9 x^{3/2}

= 2/9 x^{3/2}(3 ln √x - 1)

F(4) = 16/9 (ln 8 - 1)

F(1) = -2/9

F(4) - F(1) = 16/9 ln 8 - 14/9

**Related Questions**

Integral Calculus - Solve using Integration by Substitution : ∫√x2-...

Math - Find an equation of the line that bisects the obtuse angles formed by the...

maths... - This is the entire question: A curve has the equation y=(x+2)√(...

cal - Evaluate the integral. ∫ 28e^(√7x)/(2√x) dx

algebra 1 - alright i have a few questions if its ok..? Simplify: 1. -2√(...

Algebra - How would i complete these problems? 1. (√6mn)^5 2. ^3√16x...

maths - I will be thankfull to you if you help me to solve the below problem: 6...

Algebra Work Check - 1. 5√6 * 1/6√216 5/6 * √1296 5/6 * √...

Calculus - Find the integral by substitution ∫ [(16 x3)/(x4 + 5)] dx &#...

maths... - Differentiate ln [x+√(x^2+1)] with respect to x hence evaluate ...