JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q74

← JEE Main 2017 · 2 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 74 of 90

Let $I_n=\displaystyle\int\tan^nx\,dx$ , $(n>1)$ . If $I_4+I_6=a\tan^5x+bx^5+C$ , where C is a constant of integration, then the ordered pair (a, b) is equal to :

\left(\dfrac15,0\right)

\left(\dfrac15,-1\right)

\left(-\dfrac15,0\right)

\left(-\dfrac15,1\right)

Answer and worked solution

Official answer: A

$I_4+I_6=\int\tan^4x(1+\tan^2x)\,dx=\int\tan^4x\sec^2x\,dx=\dfrac{\tan^5x}5+C$ . So $(a,b)=\left(\frac15,0\right)$ .

Topics:Substitution

← Previous question Next question →

JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 74