WBJEE · Maths · Definite Integration
The value of \(\int_0^{\pi / 2} \frac{(\cos x)^{\sin x}}{(\cos x)^{\sin x}+(\sin x)^{\cos x}} d x\) is
- A \(\pi / 4\)
- B 0
- C \(\pi / 2\)
- D 1/2
Answer & Solution
Correct Answer
(A) \(\pi / 4\)
Step-by-step Solution
Detailed explanation
\(I=\int_0^{\pi / 2} \frac{(\cos x)^{\sin x}}{(\cos x)^{\sin x}+(\sin x)^{\cos x} d x}\) \(I=\int_0^{\pi / 2} \frac{(\sin x)^{\cos x} d x}{(\sin x)^{\cos x}+(\cos x)^{\sin x}}\) \(\Rightarrow 2 \mathrm{I}=\pi / 2\) \(\Rightarrow I=\pi / 4\)
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
- Given that \(n\) numbers of arithmetic means are inserted between two sets of numbers \(a, 2 b\) and \(2 a, b\) where \(a, b \in R\). Suppose further that the mih means between these sets of numbers are same, then the ratio \(a\) : \(b\) equalsWBJEE 2018 Medium
- If \(z=\left(\begin{array}{ccc}1 & 1+2 i & -5 i \\ 1-2 i & -3 & 5+3 i \\ 5 i & 5-3 i & 7\end{array}\right)\) then \((i=\sqrt{-1})\)WBJEE 2011 Medium
- General solution of \((x+y)^{2} \frac{d y}{d x}=a^{2}, a \neq 0\) is \((C\) is an arbitrary constant)WBJEE 2019 Medium
- If the sum of distances from a point \(\mathrm{P}\) on two mutually perpendicular straight lines is 1 unit, then the locus of \(\mathrm{P}\) isWBJEE 2010 Easy
- The straight line \(x+y-1=0\) meets the circle \(x^2+y^2-6 x-8 y=0\) at \(A\) and \(B\). Then the equation of the circle of which \(A B\) is a diameter isWBJEE 2010 Medium
- Let \(A\) and \(B\) are orthogonal matrices and \(\operatorname{det} A+\operatorname{det} B=0\). ThenWBJEE 2023 Hard
More PYQs from WBJEE
- A body of mass \(6 \mathrm{~kg}\) is acted upon by a force which causes a displacement in it given by \(x=\frac{t^2}{4}\) metre where \(t\) is the time in second. The work done by the force in 2 seconds isWBJEE 2011 Hard
- Which one of the following has the lowest ionization energy?WBJEE 2011 Easy
- The conversions(s) that can be carried out by bromine in carbon tetrachloride solvent is/areWBJEE 2023 Hard
- When \(\mathrm{H}_{2} \mathrm{O}_{2}\) is shaken with an acidified solution of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) in the presence of ether, the cthereal layer turns blue due to the formation ofWBJEE 2012 Medium
- Two blocks of \(2 \mathrm{~kg}\) and \(1 \mathrm{~kg}\) are in contact on a frictionless table. If a force of \(3 \mathrm{~N}\) is applied on \(2 \mathrm{~kg}\) block, then the force of contact between the two blocks will be :
WBJEE 2010 Medium - \(\int 2^{x}\left[f^{\prime}(x)+f(x) \log 2\right] d x\) is equal toWBJEE 2016 Hard