Explore topic-wise MCQs in Differential and Integral Calculus Questions and Answers.

This section includes 5 Mcqs, each offering curated multiple-choice questions to sharpen your Differential and Integral Calculus Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.

When solved by the method of Differentiation for the given integral i.e. \(\int_0^1 \frac{x^2-1}{log_2⁡x} dx \) the result obtained is given by _________

A. log⁡5
B. 3 log 3
C. log 4
D. 2 log 3
Answer» B. 3 log 3
Discussion
2.

Given \(f (a) = \int_a^{a^2} \frac{sin⁡ax}{x} dx \) what is the value of f’(a)?

A. \(\frac{sin⁡3a}{a}\)
B. \(\frac{3 sin⁡ a^3 – 2 sin a^2}{a}\)
C. \(\frac{3 sin a^2 – 4 sin a}{a}\)
D. \(\frac{3 sin a^3 – 3 sin^2 a}{6a}\)
Answer» C. \(\frac{3 sin a^2 – 4 sin a}{a}\)
Discussion
3.

Which among the following correctly defines Leibnitz rule of a function given by

A. \( f (α) = \int_a^b (x,α)dx\) where a & b are functions of α?
B. \(f’(α) = \int_a^b \frac{∂}{∂α} f(x,α) dx\)
C. \(f’(α) = \frac{d}{dα} \int_a^b f(x,α) dx\)
D. \(f’(α) = \int_a^b \frac{∂}{∂α} f (x,α) dx + f(b, α) \frac{da}{dα} – f(a, α) \frac{db}{dα}\)
E. \(f’(α) = \int_a^b \frac{∂}{∂α} f (x,α) dx + f(b, α) \frac{db}{dα} – f(a, α) \frac{da}{dα}\)
Answer» E. \(f’(α) = \int_a^b \frac{∂}{∂α} f (x,α) dx + f(b, α) \frac{db}{dα} – f(a, α) \frac{da}{dα}\)
Discussion
4.

Which among the following correctly defines Leibnitz rule of a function given by \( f (α) = \int_a^b (x,α)dx\) where a & b are constants?

A. \(f’(α) = \frac{∂}{∂α}\int_a^b f (x,α) dx\)
B. \(f’(α) = \frac{d}{dα} \int_a^b f (α) dx\)
C. \(f’(α) = \int_a^b \frac{∂}{∂α} f (x,α) dx\)
D. \(f’(α) = \int_a^b \frac{d}{dα} f (x,α) dx\)
Answer» D. \(f’(α) = \int_a^b \frac{d}{dα} f (x,α) dx\)
Discussion
5.

When solved by the method of Differentiation for the given integral i.e \(\int_0^∞ \frac{x^{2}-1}{log⁡x} dx\) the result obtained is given by _______

A. log⁡4
B. log⁡3
C. 2log⁡3
D. log⁡8
Answer» C. 2log⁡3
Discussion