Integration question (1 Viewer)

jimmysmith560 · Oct 31, 2022

Would the following working help for Question 2?

Note that this working answers a very similar version of this question, the only difference being that $y=ax^2$ is expressed as C, as follows:

Lith_30 · Oct 31, 2022

for question 4

we are trying to find $\int^{4}_{-4}f(x+3)dx$

as we know f(x+3) is basically f(x) shifted 3 units to the left, hence we can say that $\int^{7}_{-1}f(x)dx=\int^{4}_{-4}f(x+3)dx$ or we can use the substitution u=x+3 to show the same thing

now we can split $\int^{7}_{-1}f(x)dx$ into $\int^{7}_{0}f(x)dx+\int^{0}_{-1}f(x)dx$

using that identity given we can evaluate that $\int^{7}_{0}f(x)dx=6272$

to find $\int^{0}_{-1}f(x)dx$ we have to use the fact that f(x) is odd, which means that $\int^{0}_{-1}f(x)dx=-\int^{1}_{0}f(x)dx$ you can also get this result by using the substitution u=-x

thus $-\int^{1}_{0}f(x)dx=-2$

therefore $\int^{4}_{-4}f(x+3)dx=6272-2=6270$

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Integration question (1 Viewer)

Deem_Skills

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jimmysmith560

Le Phénix Trilingue

Lith_30

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