Question

Let

P(x)

be a polynomial of degree

n

with leading coefficient 1. Let

v(x)

be any function and

v_1(x)=

\int v(x) \mathrm{d} x

v_2(x)=\int v_1(x) \mathrm{d} x \ldots v_{n+1}(x)=\int v_n(x) \mathrm{d} x .

then

\int P(x) v(x) \mathrm{d} x

is equal to

Accepted Answer

$P(x) v_1(x)-P^{\prime}(x) v_2(x)+P^{\prime \prime}(x) v_3(x) \ldots+(-1)^n$ $n ! v_{n+1}(x)$

Answer

$P(x) v_1(x)+\frac{P^{\prime}(x) v_2(x)}{2 !}+\frac{P^{\prime \prime}(x) v_3(x)}{3 !} \ldots+\frac{v_{n+1}(x)}{(n+1) !}$

Answer

$P(x) v_1(x)+P^{\prime}(x) v_2(x)+P^{\prime \prime}(x) v_3(x) \ldots+$ $n v_{n+1}(x)$

Answer

$P(x) v_1(x)-\frac{P^{\prime}(x) v_2(x)}{2 !}+\frac{P^{\prime \prime}(x) v_3(x)}{3 !} \ldots+(-1)^n \frac{v_{n+1}(x)}{(n+1) !}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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