1
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :

Let $\rm I=\int_0^{\pi/2}\frac{f(x)}{g(x)}dx$, where f(x) = sin x and g(x) = sin x + cos x + 1

What is $\rm \int_0^{\pi/2}\frac{d(x)}{g(x)}$ equal to
1
$\frac{\ln2}{2}$
2
$\frac{\ln2}{4}$
3
ln 2
4
2 ln 2
2
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :

Let $\rm I=\int_0^{\pi/2}\frac{f(x)}{g(x)}dx$, where f(x) = sin x and g(x) = sin x + cos x + 1

What is I equal to?
1
$\rm \frac{\pi}{4}+\ln2$
2
$\rm \frac{\pi}{4}-\ln2$
3
$\rm \frac{\pi}{4}-\frac{\ln2}{2}$
4
$\rm \frac{\pi}{4}+\frac{\ln2}{2}$
3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

What is $\int^{1}_{-1}(3\sin x-\sin 3x)\cos^2 xdx$ equal to?

A

$\frac{1}{4}$

B

0

C

$\frac{1}{2}$

D

$\frac{1}{4}$

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let $p=\int_a^b f(x) d x$ and $q=\int_a^b|f(x)| d x$. If $f(x)=e^{-x}$, then which one of the following is correct ?
A

$p=2q$

B

$p=-q$

C

$4p=q$

D

$p=q$

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