AP EAMCET · Maths · Definite Integration
\(\int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x=\)
- A \(0\)
- B \(\frac{2}{15}\)
- C \(\frac{4}{15}\)
- D \(\frac{2}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{4}{15}\)
Step-by-step Solution
Detailed explanation
\(\int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x = \int_{-\pi / 2}^{\pi / 2} \sin ^3 x \cos ^2 x \, dx + \int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^3 x \, dx\) Since \(\sin^3 x \cos^2 x\) is an odd function,…
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 a man of height 1.8 mt . is walking away from the foot of a light pole of height 6 mt . with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph)AP EAMCET 2024 Easy
- From a group of men and women, the number of ways of forming a committee of members with not more than men and not less than women isAP EAMCET 2018 Medium
- If \(y=\sin ^{-1}\left[x \sqrt{1-x}-\sqrt{x} \cdot \sqrt{1-x^2}\right]\) and \(0 < x < 1\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2021 Hard
- The equation of the circle passing through the points of intersection of the circles \(x^2+y^2+4 x+6 y-12=0\) and \(x^2+y^2-6 x-4 y-12=0\) and cutting the circle \(x^2+y^2-4 x+4 y+8=0\) orthogonally isAP EAMCET 2018 Medium
- Real part of is_______AP EAMCET 2021 Medium
- If the angle between the curves \(y=e^{2(1+x)-4}\) and \(x^2 y=1\) at the point \((1,1)\) is \(\theta\), then \(|\sin \theta|+|\cos \theta|=\)AP EAMCET 2023 Medium
More PYQs from AP EAMCET
- When 80 J of heat is absorbed by a monotonic gas, its volume increases by \(16 \times 10^{-5} \mathrm{~m}^3\). The pressure of the gas isAP EAMCET 2024 Easy
- When two identical batteries of internal resistance \(1 \Omega\) each are connected in series across a resistor \(R\), the rate of heat produced in \(R\) is \(P_1\). When the same batteries are connected in parallel across \(R\), the rate of heat produced is \(P_2\). If \(\mathrm{P}_1=2.25 \mathrm{P}_2\), then the value of R isAP EAMCET 2025 Medium
- Alkenes react with water in the presence of acid to form alcohols. Identify the steps involved in the mechanism of the reaction from the following :
a) Nucleophilic addition of hydroxide ion to alkene
b) Protonation of alkene by electrophilic attack of \(\mathrm{H}_3 \mathrm{O}^{+}\)
c) Electrophilic attack of \(\mathrm{H}_2 \mathrm{O}\) on carbanion
d) Nucleophilic attack of \(\mathrm{H}_2 \mathrm{O}\) on carbocation
e) Loss of \({ }^{\ominus} \mathrm{OH}\) to form an alcohol
f) Loss of \(\mathrm{H}^{\oplus}\) to form an alcoholAP EAMCET 2017 Medium - The energies required to set up in a cube of side , A uniform electric field of and A uniform magnetic field if , are respectively aboutAP EAMCET 2018 Hard
- As shown in the figure, a block of weight \(20 \mathrm{~N}\) is connected to the top of a smooth inclined plane by massless spring of constant \(8 \pi^2 \mathrm{Nm}^{-1}\). If the block is pulled slightly from its mean position and released, the period of oscillations is
(Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )
AP EAMCET 2023 Medium - At \(500 \mathrm{~K}\), for the reaction
\(\mathrm{N}_2(g)+3 \mathrm{H}_2(g) \rightleftharpoons 2 \mathrm{NH}_3(g)\), the \(K_p\) is \(0.036 \mathrm{~atm}^{-2}\). What is its \(K_C\) in \(\mathrm{L}^2 \mathrm{~mol}^{-1}\) ?
\(\left(R=0.082 \mathrm{~L}\right.\) atom \(\left.\mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)\).AP EAMCET 2022 Easy