Mathematics - Class 12 Mock Test 6

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Question 1 of 10

1. Evaluate \(\int_0^{\pi }\)sin⁡x dx.

Question 1 of 10

Question 2 of 10

2. Find the value of \(\int_4^5 \,log⁡x \,dx\).

5-4 log⁡4-log⁡5

5 log⁡5-4 log⁡4-1

4 log⁡5-4 log⁡4-1

5 log⁡5-log⁡4+1

Question 2 of 10

Question 3 of 10

3. What is the difference property of definite integrals?

\(\int_a^b\)[f(x)+g(x)dx

\(\int_a^b\)[f(-x)+g(x)dx

\(\int_a^b\)[f(x)-g(x)dx

\(\int_a^b\)[-f(x)-g(x)dx

Question 3 of 10

Question 4 of 10

4. Compute \(\int_2^3 \frac {cos⁡x-sin⁡x}{4}\)dx.

\(\frac {1}{4}\) (sin 3 + cos 3 + sin 2 - cos 2)

\(\frac {1}{4}\) (sin 3 + cos 3 - sin 2 - cos 2)

\(\frac {1}{4}\) (sin 3 - cos 3 - sin 2 - cos 2)

\(\frac {1}{4}\) (sin 2 + cos 3 - sin 3 - cos 2)

Question 4 of 10

Question 5 of 10

5. The value of \(\int_0^{\pi }\)sin ⁡y dy is 2.

False

True

Question 5 of 10

Question 6 of 10

6. Compute \(\int_2^3\)2e^x dx.

2(e³ – e²)

84.32

2(e⁹ – e⁴)

83.25

Question 6 of 10

Question 7 of 10

7. Find \(\int_0^{\frac{π}{4}} \,9 \,cos^2⁡x \,dx\).

\(\frac{9}{4}\left (\frac{π}{2}-1\right)\)

\(\left (\frac{π}{2}-1\right)\)

\(\frac{9}{2}\left (\frac{π}{6}-1\right)\)

\(\frac{9}{4}\left (\frac{π}{2}+1\right)\)

Question 7 of 10

Question 8 of 10

8. Find \(\int_3^45x^3 \,dx\).

-\(\frac{185}{4}\)

\(\frac{185}{4}\)

-\(\frac{185}{3}\)

\(\frac{185}{2}\)

Question 8 of 10

Question 9 of 10

9. The value of \(\int_1^2\)1y⁵/5dy is _____

2.1

11.1

Question 9 of 10

Question 10 of 10

10. Find \(\int_{-2}^1 \,5x^4 \,dx\).

Question 10 of 10