Integration help (1 Viewer)

z3bra · Jul 19, 2017

Can someone please help me with q8?

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Drongoski · Jul 19, 2017

I think there is a typo in the question. The 2nd integral has to be:

$\int ^7 _0 [ f(x-3) + 2] dx$

Answer = 14

PS: Maybe not a typo; maybe the examiner who copied or set this question could not tell the error

1729 · Jul 19, 2017

z3bra said:
Can someone please help me with q8?

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$$\noindent Is the question written correctly? Because why wasn't it just written $f(x-1)$? \\\\ If this is the case then $\int_0^4 f(x)dx = \int_3^7 f(x-3)dx$ as the graph along with the bounds have all been shifted 3 units to the right. You can then split up the integral and work out $\int_3^72dx$ and sum the results. \\\\ Note: the above concerns the integral $\int_3^7\left[f(x-3) + 2\left]dx = 6 + 8 = 14$

z3bra · Jul 19, 2017

Drongoski said:
I think there is a typo in the question.

Why do u think the typo is? With the limits or where the brackets are.

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z3bra · Jul 19, 2017

1729 said:
$$\noindent Is the question written correctly? Because why wasn't it just written $f(x-1)$? \\\\ If this is the case then $\int_0^4 f(x)dx = \int_3^7 f(x-3)dx$ as the graph along with the bounds have all been shifted 3 units to the right. You can then split up the integral and work out $\int_3^72dx$ and sum the results. \\\\ Note: the above concerns the integral $\int_3^7\left[f(x-3) + 2\left]dx$

Right. Thanks ya I think your right. There's placement of brackets at wrong. Ur assumption is right and I got the right answer c. Thanks.

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Drongoski · Jul 19, 2017

z3bra said:
Why do u think the typo is? With the limits or where the brackets are.

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In the form given you won't be able to find the answer.

Drongoski · Jul 19, 2017

$$Say: $ \int f(x) dx = F(x) + C \implies F(4) - F(0) = 6\\ \\ \int _3 ^7[f(x-3) + 2] dx = \int ^7 _3 f(x-3) d(x-3) + \int ^7 _0 2dx = \left [ F(x-3) + 2x \right ]^7 _3 = (F(4) - F(0) ) + 8 = 6 + 8 = 14$

Note that we only know F(4) - F(0) = 6. We don't even know F(4) = ? and F(0) = ? much less F(a) for other values of 'a'. Hope this makes things clearer, although many would wonder about d(x-3).

Integration help (1 Viewer)

z3bra

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