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

Question

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

zepdrix · Answer

$$\large \int\limits_1^4 x(2-\sqrt x)\;dx$$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?

anonymous · Answer

thank you for your help!:)