AP EAMCET · Maths · Definite Integration
\(\int_0^{\frac{\pi}{2}} \frac{\sin \left(\frac{\pi}{4}+x\right)+\sin \left(\frac{3 \pi}{4}+x\right)}{\cos x+\sin x} d x=\)
- A \(\frac{\pi}{\sqrt{2}}\)
- B \(\frac{\pi}{2 \sqrt{2}}\)
- C \(\frac{\pi}{3 \sqrt{2}}\)
- D \(\frac{\pi}{4 \sqrt{2}}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{2 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { (b) Let } I \int \frac{-\sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}+x\right)}{\cos x \sin x} d x \\ & \Rightarrow I=\int \frac{12 \sin \left(\frac{3 \pi}{4}-x\right) \sin \left(\frac{5 \pi}{4}-x\right)}{\sin x \cos x} d x \\ & \Rightarrow…
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 \(u=\sin ^{-1}\left(\frac{x^2+y^2}{x+y}\right)\) then \(x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}\) equal to :AP EAMCET 2006 Medium
- \[
\begin{aligned}
& \text { If the } \\
& a x^2+2 h x y+b y^2+2 g x+2 f y+c=0
\end{aligned} \text { equation }
\]
represents a pair of straight lines, then the square of the distance of their point of intersection from the origin isAP EAMCET 2013 Medium - If \(a x^4+b x^3+c x^2+50 x+d=\left|\begin{array}{ccc}x^3-14 x^2 & -x & 3 x+\lambda \\ 4 x+1 & 3 x & x-4 \\ -3 & 4 & 0\end{array}\right|\), then find ' \(\lambda\) '.AP EAMCET 2020 Hard
- A point in the domain that cannot be filled in so that the resulting function is continuous is calledAP EAMCET 2020 Medium
- \(\lim _{x \rightarrow 2} \frac{\sqrt{1+4 x}-\sqrt{3+3 x}}{x^3-8}=\)AP EAMCET 2024 Easy
- If \(\cos (f(x))=\frac{1-x^2}{1+x^2}\) and \(\tan (g(x))=\frac{3 x-x^3}{1-3 x^2}\), then \(\frac{d f}{d g}=\)AP EAMCET 2019 Medium
More PYQs from AP EAMCET
- If the internal energy of 3 moles of a gas at a temperature of \(27^{\circ} \mathrm{C}\) is 2250 R, then the number of degrees of freedom of the gas is
(R - Universal gas constant)AP EAMCET 2025 Medium - If a foot of the normal from the point to a circle is and is a diameter of the circle, then the equation of circle isAP EAMCET 2021 Medium
- The figure shows three points \(A, B\) and \(C\) in a uniform electric field \((\overrightarrow{\mathrm{E}})\). The line \(\mathrm{AB}\) is perpendicular to \(\mathrm{BC}\) and \(B C\) is parallel to \(\overrightarrow{\mathrm{E}}\). If \(V_A, V_B\) and \(V_C\) are the potentials at \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) respectively, then the correct option is
AP EAMCET 2023 Easy - One of the complex roots of the equation \(x^{11}-x^6-x^5+1=0\) isAP EAMCET 2018 Medium
- If \(\frac{x}{\left(1+x^2\right)(3-2 x)}=\frac{B x+C}{1+x^2}+\frac{A}{3-2 x}\), then \(C\) isAP EAMCET 2021 Easy
- Identify the correct statements from the following
a) BOD value of clean water is less than \(5 \mathrm{ppm}\)
b) Oxidation of ethene in the presence of \(\mathrm{Pd}^{2+}\) catalyst in aqueous medium gives acetic acid
c) Photochemical smog causes damage to plant life
d) Reducing smog is a mixture of smoke, fog and \(\mathrm{SO}_2\)AP EAMCET 2017 Easy