AP EAMCET · Maths · Definite Integration
\(\int_0^\pi \frac{1}{1+\sin x} d x\) is equal to
- A 1
- B 2
- C -1
- D -2
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=\int_0^\pi \frac{1}{1+\sin x} d x \\ & =\int_0^\pi \frac{1}{1+\frac{2 \tan \frac{x}{2}}{1+\tan ^2 \frac{x}{2}}} d x \\ & =\int_0^\pi \frac{\sec ^2 \frac{x}{2}}{\left(1+\tan \frac{x}{2}\right)^2} d x \\ & \text { Put } \tan \frac{x}{2}=t…
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
- Choose the correct option regarding the following statements :
Statement I The length of common chord of the circles \(x^2+y^2+a x+b y+c=0\) and
\(x^2+y^2+b x+a y+c=0\) equals \(\frac{\sqrt{(a+b)^2-8 c}}{2}\)
Statement II If two circles intersect at two distinct points, then their radical axis is their common chord.AP EAMCET 2021 Easy - If \((2,-3,6)\) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane isAP EAMCET 2017 Easy
- The number of integer solutions of the equation isAP EAMCET 2022 Hard
- If \(\int \frac{\sin ^2 \alpha-\sin ^2 x}{\cos x-\cos \alpha} d x=f(x)+A x+B\) and \(B \in R\), thenAP EAMCET 2023 Easy
- The equation of the circle with \((1,1)\) as centre and which cuts a chord of length \(4 \sqrt{2}\) units on the line \(x+y+1=0\) isAP EAMCET 2017 Medium
- If \(z_1=-\sqrt{3}+i\) and \(z_2=-\sqrt{3}-i\) then the principal amplitude of the complex number \(\frac{z_1}{z_2}\) isAP EAMCET 2017 Easy
More PYQs from AP EAMCET
- The area of the region (in sq. units) enclosed by the curve \(y=x^3-19 x+30\) and the \(x\)-axis isAP EAMCET 2024 Easy
- The substitution \(\frac{d y}{d x}=z\), reduces the differential equation \(\frac{d^2 y}{d x^2}-\frac{d y}{d x}=0\) to a differential equation whose solution is \(\mathrm{z}=\)AP EAMCET 2022 Medium
- A metal crystallizes in simple cubic lattice. The radius of the metal atom is \(x \mathrm{pm}\). What is the volume of unit cell in \(\mathrm{pm}^3\) ?AP EAMCET 2025 Medium
- The amplitude of the side bands of the modulated signal if the carrier signal and message signal amplitudes are \(25 \mathrm{~V}\) and \(5 \mathrm{~V}\) respectively isAP EAMCET 2022 Easy
- At \(27^{\circ} \mathrm{C}\) in a \(10 \mathrm{~L}\) flask \(4.0 \mathrm{~g}\) of an ideal gaseous mixture containing. He (molar mass \(4.0 \mathrm{~g} \mathrm{~mol}^{-1}\) ) and \(\mathrm{Ne}\) (molar mass \(\left.20 \mathrm{~g} \mathrm{~mol}^{-1}\right)\) has a pres sure of \(1.23 \mathrm{~atm}\). What is the mass \(\%\) of neon ? \(\left(R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\)AP EAMCET 2017 Medium
- If \(y=\sqrt{2 x+\cos ^2\left(2 x+\frac{\pi}{4}\right)}\), then \(\frac{d y}{d x}\) at \(x=\frac{\pi}{4}\).AP EAMCET 2020 Easy