CBSE 2022 · Region 1 · Set 2 · Q1 · 2 marks
If $\displaystyle \frac{\mathrm{d}}{\mathrm{d} x}[\mathrm{~F}(x)]=\frac{\sec ^{4} x}{\operatorname{cosec}^{4} x}$ and $\displaystyle \mathrm{F}\left(\frac{\pi}{4}\right)=\frac{\pi}{4}$, then find $\displaystyle \mathrm{F}(x)$.Find : $\displaystyle \int \frac{\log x-3}{(\log x)^{4}} \mathrm{~d} x$.
If $\displaystyle \frac{\mathrm{d}}{\mathrm{d} x}[\mathrm{~F}(x)]=\frac{\sec ^{4} x}{\operatorname{cosec}^{4} x}$ and $\displaystyle \mathrm{F}\left(\frac{\pi}{4}\right)=\frac{\pi}{4}$, then find $\displaystyle \mathrm{F}(x)$.
Find : $\displaystyle \int \frac{\log x-3}{(\log x)^{4}} \mathrm{~d} x$.
Marking-scheme solution
\[\begin{aligned}
F(x) & =\int \tan ^{4} x d x=\int \tan ^{2} x \cdot\left(\sec ^{2} x-1\right) d x \\
& =\int\left(\tan ^{2} x \sec ^{2} x-\sec ^{2} x+1\right) d x \\
F(x) & =\frac{\tan ^{3} x}{3}-\tan x+x+C \\
& x=\frac{\pi}{4}, F(x)=\frac{\pi}{4} \text { gives } C=\frac{2}{3} \\
F(x) & =\frac{\tan ^{3} x}{3}-\tan x+x+\frac{2}{3}
\end{aligned}
\]
IntegralsIntegration as an Inverse Process of DifferentiationApplyvery_short_answermedium
More from Integrals
- ∫ (x+5)/((x+6)^2) e^x dx is equal to:2025 · asked 3×
- Evaluate ∫ 1/((e^x+e^-x)(e^x-e^-x)) d x log √22023 · asked 3×
- If ∫ (3 a x)/( b^2+c^2 x^2) d x=A log b^2+c^2 x^2 +K, then the value of A is2026 · asked 3×
- Find: Find: ∫ x^2 log (x^2+1) d x2023 · asked 3×
- If ∫ (2^1/x)/(x^2) d x=k · 2^1/x+C, then k is equal to2025 · asked 3×
- Find: ∫ (x^2+1)/((x-1)^2(x+3)) d x OR Evaluate: ∫ 0^π / 2 (x)/( sin x+ cos x) d x2025 · asked 3×
- Find: ∫ dx√4 x-x^22022 · asked 3×
- Find: ∫ (2 x)/((x^2+3)(x^2-5)) d x OR Evaluate: ∫ 1^4( x-2 + x-4 ) d x2025 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.