Download App

Definite Integrals — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals3 Marks
Question
Evaluate the following definite integrals:$\int_{0}^\limits{\frac{\pi}{2}}\cos^2\text{x}\text{ dx}$
✓

Answer

Let $\text{I}=\int_{0}^\limits{\frac{\pi}{2}}\cos^2\text{x}\text{ dx}$ Then,$\text{I}=\int_{0}^\limits{\frac{\pi}{2}}\cos^2\text{x}\text{ dx}$
$\Rightarrow\text{I}=\frac{1}{2}\int_{0}^\limits{\frac{\pi}{2}}(1+2\cos2\text{x})\text{dx}$ $[\because\cos2\text{x}=2\cos^2\text{x}-1\big]$
$\Rightarrow\text{I}=\Big[\frac{\pi}{2}+\frac{\sin2\text{x}}{4}\Big]^{\frac{\pi}{2}}_0$
$\Rightarrow\text{I}=\frac{\pi}{4}+0-0$
$\Rightarrow\text{I}=\frac{\pi}{4}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Definite Integrals→Definite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the area of the parallelogram whose diagonals are:
$2\hat{\text{i}}+\hat{\text{k}}$ and $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$
→
State with reasons whether the following functions have inverse:
f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}
→
Find the principal solutions of the following equations : tanθ = -1
→
Find the slope of the normal at the point 't' on the curve $\text{x}=\frac{1}{\text{t}},\text{y}=\text{t}.$
→
Solve the following differential equations:dr + (2r cot θ + sin 2θ) dθ = 0
→
Differentiate the following functions with respect to x:
$\tan^2\text{x}$
→
Evaluate the following integrals:
$\int\frac{\cos^2\text{x}-\sin^2\text{x}}{\sqrt{1+\cos4\text{x}}}\text{dx}$
→
Evaluate the following integrals:
$\int\frac{1+\cos\text{x}}{(\text{x}+\sin\text{x})^3}\text{dx}$
→
Solve the following differential equation
$\text{x}\frac{\text{dy}}{\text{dx}}+\cot\text{y}=0$
→
Three relation $R_4$ is defined in set $A = \{a, b, c\}$ as follows:
$R_4 = \{(a, b), (b, c), (c, a)\}$
Find whether or not the relation $R_4$ on A is:
  1. Reflexive.
  2. Symmetric.
  3. Transitive.
→