WBJEE · Maths · Definite Integration
The value of \(I=\int_{0}^{\frac{\pi}{4}}\left(\tan ^{n+1} x\right) d x\)
\(+\frac{1}{2} \int_{0}^{\frac{\pi}{2}} \tan ^{n+1}\left(\frac{x}{2}\right) d x\) is
- A \(\frac{1}{n}\)
- B \(\frac{n+2}{2 n+1}\)
- C \(\frac{2 n-1}{n}\)
- D \(\frac{2 n-3}{3 n-2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{n}\)
Step-by-step Solution
Detailed explanation
.Given. \(I=\int_{0}^{\pi / 4}\left(\tan ^{n+1} x\right) d x+\frac{1}{2} \int_{0}^{\pi / 2} \tan ^{n-1}\left(\frac{x}{2}\right) d x\) In second integral, putt \(=\frac{x}{2} \Rightarrow d x=2 d t\) \(\Rightarrow \quad\) Also, when \(x=0\) then \(t=0\) When \(x=\pi / 2,\) then…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(x^2+y^2=4\), then \(y \frac{d y}{d x}+x=\)WBJEE 2011 Easy
- If \(x^{2}+y^{2}=a^{2}\), then \(\int_{0}^{a} \sqrt{1+\left(\frac{d y}{d x}\right)^{2}} d x=\)WBJEE 2020 Medium
- Let \(f:[a, b] \rightarrow R\) be such that \(f\) is differentiable in \((a, b)\) is continuous at \(x=a\) and \(x=b\) and moreover \(f(a)=0=f(b)\). ThenWBJEE 2018 Medium
- \(\int \frac{\sin ^{-1} x}{\sqrt{1-x^2}} d x\) is equal to
where \(c\) is an arbitrary constantWBJEE 2009 Easy - What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any questions?WBJEE 2021 Medium
- Given \(\frac{d^2 y}{d x^2}+\cot x \frac{d y}{d x}+4 y \operatorname{cosec}^2 x=0\). Changing the independent variable \(x\) to \(z\) by the substitution \(z=\log \tan \frac{x}{2}\), the equation is changed toWBJEE 2023 Hard
More PYQs from WBJEE
-
In the circuit shown, the value of \(\beta\) of the transistor is 48 . If the base current supplied is \(200 \mu \mathrm{A}\), what is the voltage at the terminal \(\mathrm{Y}\)?WBJEE 2020 Easy - The bond order of \(\mathrm{CO}\) molecule isWBJEE 2010 Easy
- \(A B C\) is an isosceles triangle with an inscribed circle with centre \(O\). Let \(P\) be the midpoint of \(B C\). If \(A B=A C=15\) and \(B C=10\), then \(\mathrm{OP}\) equalsWBJEE 2023 Medium
- A stream of electrons and protons are directed towards a narrow slit in a screen (see figure). The intervening region has a uniform electric field (vertically downwards) and a uniform magnetic field \(\mathbf{B}\) (out of the plane of the figure) as shown. Then
WBJEE 2014 Easy - Let \(\lim _{c \rightarrow 0} \int_c^x \frac{b t \cos 4 t-a \sin 4 t}{t^2} d t=\frac{a \sin 4 x}{x}-1,(0 < x < \pi / 4)\). Then a and \(b\) are given byWBJEE 2022 Hard
- The molarity of a \(\mathrm{NaOH}\) solution by dissolving \(4 \mathrm{~g}\) of it in \(250 \mathrm{ml}\) water isWBJEE 2010 Medium