Question

\int\limits_0^1 x^3√(1+3x^4) dx

Answer 1

@ganeshie8

Answer 2

hey post it in Math group :)
http://openstudy.com/study#/groups/Mathematics

Answer 3

Okay :)

Answer 4

lets do this anyways here.. :)

Answer 5

ok thank you :)

Answer 6

u need to use 'substitution' to solve this

Answer 7

substitute \(\large u = 1+ 3x^4\)
differentiate both sides,
\(\large du = 12x^3 dx\)

\(\large \frac{1}{12}du = x^3 dx\)

Answer 8

so the given integral becomes :

\(\large \int_{0}^{1} \sqrt{u} \frac{1}{12}du\)

Answer 9

see if that looks okay so far :)

Answer 10

yeah it does then u^1/2 du?

Answer 11

:)

Answer 12

yes, since 1/12 is constant pull it out

Answer 13

\(\large \int_{0}^{1} \sqrt{u} \frac{1}{12}du\)

\(\large \frac{1}{12}\int_{0}^{1} \sqrt{u} du\)

\(\large \frac{1}{12}\int_{0}^{1} u^{\frac{1}{2}} du\)

Answer 14

now take the integral

Answer 15

\(\large \int_{0}^{1} \sqrt{u} \frac{1}{12}du\)

\(\large \frac{1}{12}\int_{0}^{1} \sqrt{u} du\)

\(\large \frac{1}{12}\int_{0}^{1} u^{\frac{1}{2}} du\)

\(\large \frac{1}{12} \frac{u^{\frac{1}{2}+1} }{\frac{1}{2}+1}\Big|_{0}^{1}\)

Answer 16

lets simplify further, before evaluating the bounds

Answer 17

\(\large \int_{0}^{1} \sqrt{u} \frac{1}{12}du\)

\(\large \frac{1}{12}\int_{0}^{1} \sqrt{u} du\)

\(\large \frac{1}{12}\int_{0}^{1} u^{\frac{1}{2}} du\)

\(\large \frac{1}{12} \frac{u^{\frac{1}{2}+1} }{\frac{1}{2}+1}\Big|_{0}^{1}\)

\(\large \frac{1}{12} \frac{u^{\frac{3}{2}} }{\frac{3}{2}}\Big|_{0}^{1}\)

\(\large \frac{1}{18} u^{\frac{3}{2}}\Big|_{0}^{1}\)

\(\large \frac{1}{18} (1+3x^4)^{\frac{3}{2}}\Big|_{0}^{1}\)

Answer 18

now you're ready to evaluate the bounds..

Answer 19

\(\large \int_{0}^{1} \sqrt{u} \frac{1}{12}du\)

\(\large \frac{1}{12}\int_{0}^{1} \sqrt{u} du\)

\(\large \frac{1}{12}\int_{0}^{1} u^{\frac{1}{2}} du\)

\(\large \frac{1}{12} \frac{u^{\frac{1}{2}+1} }{\frac{1}{2}+1}\Big|_{0}^{1}\)

\(\large \frac{1}{12} \frac{u^{\frac{3}{2}} }{\frac{3}{2}}\Big|_{0}^{1}\)

\(\large \frac{1}{18} u^{\frac{3}{2}}\Big|_{0}^{1}\)

\(\large \frac{1}{18} (1+3x^4)^{\frac{3}{2}}\Big|_{0}^{1}\)

\(\large \frac{1}{18} [(1+3)^{\frac{3}{2}} - 1]\)

\(\large \frac{1}{18} [8 - 1]\)

\(\large \frac{1}{18} [7]\)

Answer 20

see if that makes soem sense :)

Answer 21

whatever u will do,will always make sense lol :) seriously u are a genius :)

Answer 22

nope, you're a genus to learn so fast :) im glad it made sense =))

Answer 23

I was not, never will be :) i have no brain.. thank you ganeshie :)

Answer 24

i dont think so...
you're super fine and on right track learning stuff...
okay lets skip it lol :)

Answer 25

okay thank you very much for helping :)

Answer 26

np :)

Answer 27

:)