Question

Find ∫ 6√x dx, and hence evaluate

Answer 1

\[\int\limits_{4}^{1}6\sqrt{x}dx\]

Answer 2

My book says the answer is \[4x \sqrt{x}; 28\]

Answer 3

Rewrite the definite integral replacing the sqrt(x) with \[x ^{\frac{ 1 }{ 2 }}.\]

Answer 4

Your integral will now look like \[6 \int\limits_{}^{}x ^{\frac{ 1 }{ 2 }}dx\]

Answer 5

Use the Power Rule for Integration.

Answer 6

Are you sure it's not [1,4],rather than [4,1]?

Answer 7

I mean \[\int\limits_{1}^{4}6\sqrt{x}dx\]

Answer 8

\[\int\limits_{1}^{4} 6\sqrt{x} dx \implies \int\limits_{1}^{4} 6x^{1/2} dx \] Taking the integral you get \[\huge \implies \frac{ 6x^{1/2+1} }{ {1/2+1} } |_1^4\]

Answer 9

I leave the simplification to you :)