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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Indefinite Integration

NTA Abhyas 2020 · Mathematics · Indefinite Integration

If ∫ 2x^ 2 + 5 x^ 2 + a dx = f (x) , where f (x) is a polynomial or...

If

∫ \dfrac{2x^{2} + 5}{x^{2} + a}dx = f \left(x\right)

, where

f \left(x\right)

is a polynomial or ratio of polynomials, then the number of possible value(s)

of a

is equal to

Options

A $0$
B $1$
C $2$
D $3$

Correct answer

C. $2$

Step-by-step solution

f\left(x\right) = ∫ \dfrac{2\left(x^{2} + a\right) + \left(5 - 2a\right)}{x^{2} + a}dx

= 2x + \left(5 - 2a\right)∫ \dfrac{dx}{x^{2} + a}

If

f\left(x\right)

is polynomial,

a = \dfrac{5}{2}

If

f \left(x\right)

is ratio of polynomials,

a = 0

Therefore, the possible values of

a

is

2

.

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