AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\sin 2 x d x}{\sin ^4 x+\cos ^4 x}=\tan ^{-1}(f(x))+c\), then \(f\left(\frac{\pi}{3}\right)=\)
- A 1
- B 2
- C 3
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
Let \[ \begin{aligned} I & =\int \frac{\sin 2 x d x}{\sin ^4 x+\cos ^4 x} \\ & =\int \frac{2 \sin x \cos x}{\sin ^4 x+\cos ^4 x} d x \end{aligned} \] Dividing by \(\cos ^2 x\) in numerator and denominator, we get…
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 \(\int_0^{2 \pi}|x \sin x| d x=k \pi\), then \(k=\)AP EAMCET 2023 Medium
- If \(|z-3 i|+|z+5 i|=4\), then the locus of \(z\) isAP EAMCET 2022 Medium
- If the median AD of the triangle ABC is bisected at E and BE meets AC in F, then \(\mathrm{AF}: \mathrm{AC}=\)AP EAMCET 2025 Medium
- In the binomial expansion of \((a-b)^n, n \geq 5\), the sum of the \(5^{\text {th }}\) and \(6^{\text {th }}\) terms is zero. Then the value of \(\frac{a}{b}\) isAP EAMCET 2020 Easy
- \(\int \frac{x^8+4}{x^4-2 x^2+2} d x=A x^5+B x^3+C x+k\), then \(5 A+3 B+C=\)AP EAMCET 2022 Medium
- \(\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x=\)AP EAMCET 2024 Medium
More PYQs from AP EAMCET
- The kinetic energy of a particle executing simple harmonic motion at a displacement of 3 cm from the mean position is 4 mJ. If the amplitude of the particle is 5 cm, then the maximum force acting on the particle isAP EAMCET 2025 Medium
- The stationary points of the curve are____AP EAMCET 2021 Easy
- If \(P+Q+R=\frac{\pi}{4}\), then
\(\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos \left(\frac{\pi}{8}-R\right)=\)AP EAMCET 2024 Hard - Assertion (A) At critical temperature, surface tension of liquids become zero.
Reason (R) At critical temperature, intermolecular forces for liquids and gases become equal.AP EAMCET 2021 Medium - If \(A\) and \(B\) are events of a random experiment with \(P(A)\) \(=0.5, \mathrm{P}(\mathrm{B})=0.4\) and \(\mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.3\), then the probability that neither A nor B occurs isAP EAMCET 2023 Easy
- The equation of a stationary wave is \(y=20 \sin (\pi x)\) \(\cos (\omega t)\), where \(x, y\) are in metre and \(t\) is in second. The distance between a node and its adjacent antinode isAP EAMCET 2023 Easy