11For the 2nd Qsn, the best way to proceed is by graphs....
The area enclosed between 2 functions f(x) & g(x) is basically \int_{k}^{l}{|f(x)-g(x)|}dx.
So now Q2 is damn simple. I hope.
Q1 \ \int \frac{dx}{x^{22}(x^7-6)}
Q2 \ Let \ t(x)=u(x)-v(x) \ where \ u(x)=sin^62\pi x \ and \ v(x)=lnx
Prove \ area \ enclosed \ by \ u(x) \ and \ v(x) \ is
\sum_{r=0}^{n}{\int_{x_r}^{x_{r+1}}{(-1)^r.t(x)dx}} \ where \ x_0,x_1...x_{n+1} \ are \ roots \ of \ u(x)=v(x) \ in \ increasing \ order
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2 Answers
29in qn 1 multiply the numerator and denominator by X6 and then take x7 = t ..after that use partial fraction..u will get the answer
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