MHT CET · Maths · Definite Integration

\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \frac{\cos x}{1+e^x} d x=\)

A 1
B 2
C -1
D 0

Verified Solution

Answer & Solution

Correct Answer

(A) 1

Step-by-step Solution

Detailed explanation

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

If the slopes of the lines given by the equation \(a x^{2}+2 h x y+b y^{2}=0 \quad\) are in the
ratio \(5: 3\), then the ratio \(h^{2}: a b=\)

MHT CET 2020 Easy
If \(\mathrm{y}=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]\), then \(\frac{d y}{d x}=\)

MHT CET 2020 Hard
If the lines \(4 x+3 y-1=0, x-y+5=0\) and \(k x+5 y-3=0\) are concurrent, then \(k=\)

MHT CET 2022 Easy
If \(y=\tan ^{-1}\left(\frac{5 x+1}{3-x-6 x^2}\right)\), then \(\frac{d y}{d x}=\)

MHT CET 2022 Medium
If the probability distribution function of a random variable is given as

Then \(F(0)=\) _____________

MHT CET 2016 Hard
If \(\tan \theta=\frac{\sin \alpha-\cos \alpha}{\sin \alpha+\cos \alpha}, 0 \leq \alpha \leq \frac{\pi}{2}\), then the value of \(\cos 2 \theta\) is

MHT CET 2023 Easy

Explore more questions on app

From MHT CET

In an interference experiment, the spacing between successive maxima or minima is

MHT CET 2008 Easy
Match the following in Column I with the means adopted to tide over periods of unfavorable conditions in Column II.
Colum I Column II
i Birds a. Dormancy
ii. Seeds b. Hibernation
iii. Snails c. Migration
iv. Polar bear d. Aestivation

MHT CET 2023 Easy
The value of \(\int \frac{\left(x^2-1\right) \mathrm{d} x}{x^3 \sqrt{2 x^4-2 x^2+1}}\) is

MHT CET 2023 Hard
Calculate the cryoscopic constant of solvent if depression in freezing point of 0.4 m solution of nonvolatile solute is 1.8 K .

MHT CET 2025 Easy
Cambium is essential for grafting in plants because

MHT CET 2018 Hard
In the given circuit, when \(S_1\) is closed, the capacitor \(C\) gets full charged. Then \(S_1\) is kept open and \(S_2\) is closed. Hence

MHT CET 2022 Hard

Explore more questions on app

	Colum I		Column II
i	Birds	a.	Dormancy
ii.	Seeds	b.	Hibernation
iii.	Snails	c.	Migration
iv.	Polar bear	d.	Aestivation