AP EAMCET · Maths · Definite Integration
\(\tan ^{-1}\left[\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x\right]=\)
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{6}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
Given, \(\tan ^{-1}\left[\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos x}{1+e^x} d x\right]\) Let \(I=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos x}{1+e^x} d x\)...(i)…
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
- A pair of lines \(S=\mathbf{0}\) together with the lines given by the equation \(8 x^2-14 x y+3 y^2+10 x+10 y-25=0\) form a parallelogram. If its diagonals intersect at the point \((3,2)\), then the equation \(S=0\), isAP EAMCET 2019 Medium
- If in the angles of a triangle are in the ratio \(1: 1: 4\), then the ratio of the perimeter of the triangle to its largest side isAP EAMCET 2014 Hard
- If \(p\) th, \(q\) th, \(r\) th terms of a geometric progression are the positive numbers \(a, b\) and \(c\) respectively, then the angle between the vectors \(\left(\log a^2\right) \mathbf{i}+\left(\log b^2\right) \mathbf{j}+\left(\log c^2\right) \mathbf{k} \quad\) and \((q-r) \mathbf{i}+(r-p) \mathbf{j}+(p-q) \mathbf{k}\) isAP EAMCET 2012 Hard
- The equation of the straight line perpendicular to the straight line \(3 x+2 y=0\) and passing through the point of intersection of the lines \(x+3 y-1=0\) and \(x-2 y+4=0\) isAP EAMCET 2009 Easy
- For the matrix \(A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right] \cdot A^{-1}=\)AP EAMCET 2018 Easy
- If the point divides the line segment joining the points and in the ratio thenAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- The number of subsets of \(\{1,2,3, \ldots, 9\}\) containing at least one odd number isAP EAMCET 2009 Medium
- The ends of an element of zinc wire are kept at a small temperature difference \(\Delta T\) and a small current \((I)\) is passed through the wire. Then, the heat developed per unit timeAP EAMCET 2013 Easy
- A pair of lines \(S=\mathbf{0}\) together with the lines given by the equation \(8 x^2-14 x y+3 y^2+10 x+10 y-25=0\) form a parallelogram. If its diagonals intersect at the point \((3,2)\), then the equation \(S=0\), isAP EAMCET 2019 Medium
- \(\sin ^2 5^{\circ}+\sin ^2 10^{\circ}+\sin ^2 15^{\circ}+\ldots+\sin ^2 90^{\circ}\) is equal toAP EAMCET 2021 Easy
- If the point \(P(\alpha, \beta, \gamma)\) lies on the plane \(2 x+y+z=1\) and \([\alpha \beta \gamma]\left[\begin{array}{lll}1 & 9 & 1 \\ 8 & 2 & 1 \\ 7 & 3 & 1\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]\), then \(\alpha^2+\beta^2+\gamma^2=\)AP EAMCET 2018 Medium
- Let \(A\) and \(B\) represent \(z_1\) and \(z_2\) in the Argand plane and \(z_1, z_2\) be the roots of the equation \(Z^2+p Z+q=0\), where \(p, q\) are complex numbers. If \(O\) is the origin, \(O A=O B\) and \(\lfloor A O B=\alpha\), then \(p^2=\)AP EAMCET 2017 Hard