CBSE 2022 · Region 5 · Set 3 · Q9 · 3 marks
Evaluate : $\displaystyle \int_{1}^{3} \frac{\sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}}+\sqrt{4-\mathrm{x}}} \mathrm{dx}$
Marking-scheme solution
\[\begin{aligned}
I & =\int_{1}^{3} \frac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}} d x \\
& =\int_{1}^{3} \frac{\sqrt{4-x}}{\sqrt{4-x}+\sqrt{x}} d x \quad \text { (using property) } \\
& \left.\Rightarrow 2 I=\int_{1}^{3} 1 d x=x\right]_{1}^{3}=2 \\
& \Rightarrow I=1
\end{aligned}
\]
IntegralsSome Properties of Definite IntegralsApplyshort_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.