✓ Board-verified
Mathematics · 2022 · 2 marks
CBSE 2022 · Region 2 · Set 1 · Q2
(a) Find: ∫ (sin 3 x)/(sin x) d x
(a)
Find : \[\int \frac{\sin 3 \mathrm{x}}{\sin \mathrm{x}} d \mathrm{x} \]
OR
(b)
Evaluate : \[\int_{0}^{\frac{1}{2} \log 3} \frac{\mathrm{e}^{\mathrm{x}}}{\mathrm{e}^{2 \mathrm{x}}+1} \mathrm{dx} \]
Marking-scheme solution
(a)
\[\int \frac{\sin 3x}{\sin x}\,dx = \int \frac{3\sin x - 4\sin^3 x}{\sin x}\,dx\]
\[= \int \left[3 - 4\frac{(1-\cos 2x)}{2}\right] dx\]
\[= \int (1 + 2\cos 2x)\,dx\]
\[= x + \sin 2x + C\]
Or(b) Let $\displaystyle e^x = t$, $\displaystyle e^x dx = dt$
\[\therefore \int_{0}^{\frac{1}{2}\log 3} \frac{e^x}{e^{2x}+1}\,dx = \int_{1}^{\sqrt{3}} \frac{dt}{t^2+1}\]
\[= \tan^{-1} t \Big|_{1}^{\sqrt{3}}\]
\[= \frac{\pi}{3} - \frac{\pi}{4} = \frac{\pi}{12}\]
More from Integrals
- Evaluate: ∫_0^π x/(1+ sin x) d x2022 · asked 2×
- Evaluate ∫_-1^1|x^4-x| d x. OR Find ∫ (sin^-1 x)/((1-x^2)^3 / 2) d x.2023
- Find: ∫ (x^2)/((x^2+4)(x^2+9)) d x2023
- Evaluate: ∫_0^π (sin^2026 x)/(sin^2026 x+ cos^2026 x) d x2026
- Evaluate: ∫_1^3 (√x)/(√x+√(4-x)) dx2022
- Find: ∫ ((3 cos x-2) sin x)/(5- sin^2 x-4 cos x) d x OR Evaluate: ∫_-2^2 (x^3+|x|+1)/(x^2+4|x|+4) d x2024
- ∫ (x+5)/((x+6)^2) e^x dx is equal to:2025
- Evaluate ∫ 1/((e^x+e^-x)(e^x-e^-x)) d x log √22023
CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.