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Intergration by parts (IBP). - This accours every time you have a mulitplication in an intergral. This quesion wants you to find the area under the graph x²e^x. For any intergration b...

Given that you have a fraction in the question, you are clearly asked to use the quotient rule. In order to do this, you should label the numerator u, and the denominator v, like this: u = 2x v=cos(x). No...

would use paper to show the student the final answer Your answer will be based around the graph of y=sin(x), which has a y maximum of 1 and minimum of -1, and one full cycle is completed by 2 pi....

Firstly we look at the term 2(x^3). The power of x (in this case 3) is multiplied by the factor of x (in this case 2) and the power is then reduced by 1. This means it is 2x3(x^{3-1}) which simplifies to ...

First, multiply all terms by (x - 1) to remove the quotient, and multiply out of the brackets: 3x + 2 + 3(x - 1) = 4(x - 1) >>> 3x + 2 + 3x - 3 = 4x - 4. Next, group all like terms on either side...