Question

x(2-squareroot of x)dx x=4 (upper limit) 1 lower limit

Answer 1

\[\large \int\limits_1^4 x(2-\sqrt x)\;dx\]Distribute the x to each term inside the brackets.\[\large \int\limits\limits_1^4 2x-x\sqrt x\;dx\]Rewrite the squareroot as a rational expression,\[\large \int\limits\limits\limits_1^4 2x-x\cdot x^{1/2}\;dx\]Remember how to multiply terms of the same base? We add the exponents.\[\large \int\limits\limits\limits\limits_1^4 2x-x^{1+1/2}\;dx \qquad = \qquad \int\limits\limits\limits\limits_1^4 2x-x^{3/2}\;dx\]

Then simply apply the `Power Rule for Integration`. Understand how to proceed?

Answer 2

thank you for your help!:)