Checking work on changing the boundaries of a definite integral
(I have been taught to sub back, but going over this approach now)

Question

Checking work on changing the boundaries of a definite integral
(I have been taught to sub back, but going over this approach now)

idku · Answer

$$2\int\limits_{4}^{11}x(x^2-15)^3~dx$$

idku · Answer

$$\color{blue}{u=x^2-15}$$$$x=4,~~~~~~~\Rightarrow~~~~~~~u=4^2-15~~~~~~~\Rightarrow~~~~~~~u=1$$$$x=11,~~~~~\Rightarrow~~~~~u=11^2-15~~~~~\Rightarrow~~~~~u=121-15~~~~~\Rightarrow~~~~~u=106$$$$\color{blue}{du=2x~dx}$$

$$\int\limits_{1}^{106}u^3~du$$

idku · Answer

So, now all what I have to do is to integrate it (without subbing the x back into the equation.

$$=\frac{1}{4}(106)^4-(1)^4$$and then just a calculation.

idku · Answer

@whpalmer4 @triciaal can you guys check my work please?

idku · Answer

oh 1/4 next to (1)^4.

idku · Answer

but anything other than this?

whpalmer4 · Answer

appears to get the right answer

idku · Answer

(Wouldn't use geometric shapes on this one, whether on the one with u's or x's)
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