11) for \int_{3}^{7} f^{-1}(x) dx take x = f(t) to get,
\int_{2}^{5} t.f'(t) dt ..now use by parts to get the answer.
2) rewrite as 100C2 + 99C2....
this is coeff of x^2 in (1+x)100 + (1+x)99...
use gp formula to get.
let f be a one to one continuous function such that f(2) =3and f(5)=7. given (2to5)∫ f(x) dx =17
then value of (3to7)∫ f-1(x) dx is
(a) 10
(b) 11
(c)12
(d) 13
ans c
2 if nCk is cmbination of n diff. thing taking k at a time then value of
100 C 98 + 99 C 97 + 98 C 96 + .............. + 3C 1 + 2C 0
ans 166650
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2 Answers
1
1708(1) 
\hspace{-16}$Here $\bold{Yellow\; Part\Leftrightarrow }\bf{\int_{2}^{5}f(x)dx=17}$\\\\\\ and $\bold{Red\;Part\Leftrightarrow }\bf{\int_{3}^{7}f^{-1}(x)dx}$\\\\\\ So $\bf{\int_{3}^{7}f^{-1}(x)dx}=12$
