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Calculus/Evaluating an integral

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Expert: - 8/3/2010


Question

integral
Evaluate the integral

Answer
Hi Michelle,
We'll work it out by the method of substitution.
Let u = √x
du/dx = 1/2√x = 1/2u
dx = 2u du
As for the limits,
at x = 1, u = 1
at x = 4, u = 2
Now,
∫(x² + 6)/√x dx  from 1 to 4  =  ∫(u^4 + 6)/u . 2u du  from 1 to 2
= 2∫(u^4 + 6) du  from 1 to 2
= 2[u^5/5 + 6u]  from 1 to 2
= 2[2^5/5 + 6(2)] - 2[1^5/5 + 6(1)]
= 36.8 - 12.4
= 24.4 sq. units

Note that the indefinite integral ∫(x² + 6)/√x dx is simply  
2[u^5/5 + 6u] = 2u(u^4/5 + 6) + C
             = 2√x(x²/5 + 6) + C

Regards

Ahmed Salami

Expertise

I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I believe i would be very helpful in calculus and can as well help a good deal in Physics with most emphasis directed towards mechanics.

Experience

An engineering graduate. I have been doing maths and physics all my life.

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