Easy Integral

Calculus Level 1

$\huge \int _{ 4 }^{ 12 }{ { x }^{ 3 }dx } =?$

The answer is 5120.

3 solutions

Mehul Arora
Sep 2, 2015

$\huge \int _{ a }^{ b }{ { x }^{ n }dx } ={ \left( \frac { { x }^{ n+1 } }{ n+1 } \right) }_{ a }^{ b }=\frac { 1 }{ 4 } \left( { 12 }^{ 4 }-{ 4 }^{ 4 } \right)$

Here, $n \neq -1$

$\huge =5120$

@Mehul Arora Done with calculus also? Cool!

Anik Mandal - 5 years, 9 months ago

you should mention that n cannot be equals to -1.

Pi Han Goh - 5 years, 9 months ago

Pretty sure he did if you look at the bottom

Liam Bennett - 5 years, 9 months ago

Actually, I edited it after he told me to do so :)

Mehul Arora - 5 years, 9 months ago

Aye Chan Ko
Sep 2, 2015

Integrate this and we get ((12^4)/4)-((4^4)/4).
12 is 4 * 3 and so ((4^4)*(3^4)/4)-((4^4)/4)
(4^4)/4 is 4^3 and so
=4^3 (3^4 -1)
=64 * 80
=5120

Eashan Mundhe
Sep 9, 2015

integral of x power n with respect to x is (x power n+1 )/(n+1) hence the answer is x power 4 divided by 4 with limits 12 and 4 as upper and lower limits hence 12 power 4 divided by 4 - 4 power 4 divided by 4 is the answer i.e 5184-64=5120

Easy Integral

The answer is 5120.

3 solutions

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