1.

If `intf(x)dx=g(x),then intx^(11)f(x^(6))dx` is equal toA. `1/6[x^(6)g(x^(6))-intx^(5)g(x^(6))]+C`B. `1/6x^(6)g(x^(6))-intx^(5)g(x^(6))dx+C`C. `1/6[x^(6)g(x^(6))-5intx^(5)g(x^(6))dx]+C`D. None of these

Answer» Correct Answer - 2
`I=intx^(11)f(x^(6))dx`
put `x^(6)=trArr6x^(5)dx=dt`
`I=1/6inttf(t)dt`
`=1/6[tg(t)-intg(t)dt]`
`=1/6[x^(6)g(x^(6))-intg(x^(6))d(x^(6))]`
`=1/6[x^(6)g(x^(6))-6intx^(5)g(x^(6))dx]`
`=1/6x^(6)g(x^(6))-intx^(5)g(x^(6))dx+C`


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