Available Questions 24 found Page 1 of 2
Standalone Questions
#1482
Mathematics
Definite Integrals
LA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Evaluate: $\int_{0}^{\pi}\frac{x\tan x}{\sec x+\tan x}dx$
Key:
Sol:
Sol:
#1460
Mathematics
Definite Integrals
LA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Evaluate: $\int_{0}^{\pi/2}\frac{x}{\sin x+\cos x}dx$.
Key:
Sol:
Sol:
#1430
Mathematics
Definite Integrals
SA
APPLY
2025
AISSCE(Board Exam)
Competency
3 Marks
Evaluate: $\int_{1}^{4}(|x-2|+|x-4|)dx$.
Key:
Sol:
Sol:
#1418
Mathematics
Definite Integrals
LA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Evaluate: $\int_{0}^{\pi}\frac{dx}{a^{2}\cos^{2}x+b^{2}\sin^{2}x}$.
Key:
Sol:
Sol:
#1410
Mathematics
Definite Integrals
SA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate: $\int_{\pi/2}^{\pi}e^{x}\left(\frac{1-\sin x}{1-\cos x}\right)dx$.
Key:
Sol:
Sol:
#1379
Mathematics
Definite Integrals
VSA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Evaluate: $\int_{0}^{\frac{\pi}{4}}\sqrt{1+\sin 2x}dx$.
Key:
Sol:
Sol:
#1365
Mathematics
Definite Integrals
SA
2025
AISSCE(Board Exam)
3 Marks
Evaluate: $\int_{0}^{\frac{\pi}{4}}\frac{dx}{\cos^{3}x\sqrt{2\sin 2x}}$.
Key:
Sol:
Sol:
#1343
Mathematics
Definite Integrals
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate : $\int_{0}^{\pi}\frac{e^{cos~x}}{e^{cos~x}+e^{-cos~x}}d~x$
Key:
Sol:
Sol:
#1318
Mathematics
Definite Integrals
SA
APPLY
2024
AISSCE(Board Exam)
Competency
3 Marks
Evaluate $\int_{0}^{\frac{\pi}{4}}\frac{x~dx}{1+cos~2x+sin~2x}$
Key:
Sol:
Sol:
#1307
Mathematics
Definite Integrals
LA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Evaluate: $\int_{0}^{\frac{\pi}{2}}sin~2x~tan^{-1}(sin~x)dx$
Key:
Sol:
Sol:
#1306
Mathematics
Definite Integrals
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Evaluate: $\int_{0}^{\frac{\pi}{4}}\frac{sin~x+cos~x}{9+16~sin~2x}dx$
Key:
Sol:
Sol:
#1300
Mathematics
Definite Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate: $\int_{1}^{3}(|x-1|+|x-2|+|x-3|)dx$
Key:
Sol:
Sol:
#1292
Mathematics
Definite Integrals
VSA
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Evaluate: $\int_{0}^{\frac{\pi^{2}}{4}}\frac{sin\sqrt{x}}{\sqrt{x}}dx$
Key:
Sol:
Sol:
#1275
Mathematics
Definite Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate : $\int_{-2}^{2}\sqrt{\frac{2-x}{2+x}}dx$
Key:
Sol:
Sol:
#1257
Mathematics
Definite Integrals
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Evaluate: $\int_{0}^{\pi/4}\frac{1}{sin~x+cos~x}dx$
Key:
Sol:
Sol:
#1247
Mathematics
Definite Integrals
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Evaluate: $\int_{0}^{\pi/2}sin~2x~cos~3x~dx$
Key:
Sol:
Sol:
#636
Mathematics
Definite Integrals
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If \(f(2a-x)=f(x)\), then \(\int_{0}^{2a}f(x)dx\) is
(A) \(\int_{0}^{2a}f(\frac{x}{2})dx\)
(B) \(\int_{0}^{a}f(x)dx\)
(C) \(2\int_{a}^{0}f(x)dx\)
(D) \(2\int_{0}^{a}f(x)dx\)
Key:
Sol:
Sol:
**Correct Option if MCQ:** D
**Reasoning:**
* Let \(I = \int_{0}^{2a}f(x)dx\).
* Using the property \(\int_{0}^{na}f(x)dx = n\int_{0}^{a}f(x)dx\) for \(f(x)=f(2a-x)\).
* Thus, \(I = 2\int_{0}^{a}f(x)dx\).
#635
Mathematics
Definite Integrals
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The value of \(\int_{0}^{1}\frac{dx}{e^{x}+e^{-x}}\) is:
(A) \(-\frac{\pi}{4}\)
(B) \(\frac{\pi}{4}\)
(C) \(\tan^{-1}e-\frac{\pi}{4}\)
(D) \(\tan^{-1}e\)
Key: C
Sol:
Sol:
\[\frac{1}{e^{x}+e^{-x}} = \frac{1}{e^{x} + \frac{1}{e^{x}}} = \frac{1}{\frac{e^{2x} + 1}{e^x}} = \frac{e^x}{e^{2x} + 1}\]
The integral becomes:
\[I = \int_{0}^{1}\frac{e^x}{e^{2x} + 1}dx\]Now use Substitution
Let \(u = e^x\). Then, \(du = e^x dx\).
Change the limits of integration:
- Lower limit (\(x=0\)): \(u_1 = e^0 = 1\)
- Upper limit (\(x=1\)): \(u_2 = e^1 = e\)
The integral becomes:
\[I = \int_{1}^{e}\frac{du}{u^{2} + 1}\]Now evaluate and Apply Limits
\[I = \left[ \tan ^{-1}(u) \right]_{1}^{e}\] \[=\tan ^{-1}(e) - \frac{\pi}{4}\]
#634
Mathematics
Definite Integrals
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
\(\int_{0}^{\pi/2}\cos x\cdot e^{\sin x}dx\) is equal to:
(A) 0
(B) \(1-e\)
(C) \(e-1\)
(D) e
Key:
Sol:
Sol:
#633
Mathematics
Definite Integrals
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
\(\int_{a}^{b}f(x)dx\) is equal to:
(A) \(\int_{a}^{b}f(a-x)dx\)
(B) \(\int_{a}^{b}f(a+b-x)dx\)
(C) \(\int_{a}^{b}f(x-(a+b))dx\)
(D) \(\int_{a}^{b}f((a-x)+(b-x))dx\)
Key:
Sol:
Sol: