engineering recuitment NIMCET Previous Year Papers Mock Test Mathematics Integral Calculus Indefinite Integrals
If \(\rm \displaystyle I_n = \int_0^a(a^2 - x^2)^n \ dx\), where n is a positive integer, then the relation between In and In-1 is:
1
\(\rm I_n = \left(\dfrac{2na^2}{2n+1}\right)I_{n-1}\)
2
\(\rm I_n = \left(\dfrac{2n^2a^2}{2n+1}\right)I_{n-1}\)
3
\(\rm I_n = \left(\dfrac{2na^2}{2n-1}\right)I_{n-1}\)
4
\(\rm I_n = \left(\dfrac{2n^2a^2}{2n-1}\right)I_{n-1}\)