WBJEE · Maths · Definite Integration

The value of \(I=\int_{-\pi / 2}^{\pi / 2}|\sin x| d x\) is

A 0
B 2
C -2
D \(-2 < \) I \( < 2\)

Verified Solution

Answer & Solution

Correct Answer

(B) 2

Step-by-step Solution

Detailed explanation

Hints: \(I=2 \int_0^{\frac{\pi}{2}} \sin x d x=2(1)=2\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Let \(P(4,3)\) be a point on the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=\mathrm{1}\). If the normal at \(P\) intersects the \(X\) -axis at (16,0) , then the eccentricity of the hyperbola is

WBJEE 2019 Medium
If the coefficient of \(x^{8}\) in \(\left(a x^{2}+\frac{1}{b x}\right)^{13}\) is equal to the coefficient of \(x^{-8}\) in \(\left(a x-\frac{1}{b x^{2}}\right)^{13},\) then \(a\) and \(b\) will satisfy the relation

WBJEE 2014 Medium
The value of \(\int_0^{\infty} \frac{d x}{\left(x^2+4\right)\left(x^2+9\right)}\) is

WBJEE 2009 Hard
Let \(f: R \rightarrow R\) be given by \(f(x)=\left|x^{2}-1\right|, x \in R\). then

WBJEE 2021 Easy
If \(g(f(x))=|\sin x|\) and \(f(g(x))=(\sin \sqrt{x})^2\), then

WBJEE 2025 Medium
If \(y=\log ^n x\), where \(\log ^n\) means \(\log _e \log _e \log _e \ldots\) (repeated \(n\) times), then \(x \log x \log ^2 x \log ^3 x \ldots . . \log ^{n-1} x \log ^n x \frac{d y}{d x}\) is equal to

WBJEE 2023 Medium

Explore more questions on app

From WBJEE

The displacement of a particle in a periodic motion is given by \(y=4 \cos ^{2}\left(\frac{t}{2}\right) \sin (1000 t)\). This displacement may be considered as the result of superposition of \(n\) independent harmonic oscillations. Here \(n\) is

WBJEE 2014 Medium
A copper coin was electroplated with \(\mathrm{Zn}\) and then heated at high temperature until there is a change in colour. What will be the resulting colour?

WBJEE 2019 Easy
Let \(\vec{\alpha}, \vec{\beta}, \vec{\gamma}\) be the three unit vectors such that \(\vec{\alpha} \cdot \vec{\beta}=\vec{\alpha} \cdot \vec{\gamma}=0\) and the angle between \(\vec{\beta}\) and \(\vec{\gamma}\)
is \(30^{\circ} .\) Then \(\vec{\alpha}\) is

WBJEE 2018 Easy
A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by \(1 \%\). If the Poisson's ratio for the material of the rod be \(0.2,\) which of the following statements is correct? "The volume approximately ...........

WBJEE 2019 Medium
The line \(y-\sqrt{3} x+3=0\) cuts the parabola \(y^2=x+2\) at the points \(P\) and \(Q\). If the co-ordinates of the point \(X\) are \((\sqrt{3}, 0)\), then the value of \(X P \cdot X Q\) is

WBJEE 2025 Medium
A double ordinate \(\mathrm{PQ}\) of the hyperbola \(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1\) is such that \(\Delta \mathrm{OPQ}\) is equilateral, \(\mathrm{O}\) being the centre of the hyperbola. Then the eccentricity e satisfies the relation

WBJEE 2020 Easy

Explore more questions on app