FAQs on Integrals of Some Particular Functions

Question 1

1. What is the integral of a constant function?

Accepted Answer

Ans. The integral of a constant function is simply the constant multiplied by the variable of integration. For example, if the constant is 'a' and the variable of integration is 'x', the integral would be 'ax + C', where C is the constant of integration.

Question 2

2. How do you find the integral of a power function?

Accepted Answer

Ans. To find the integral of a power function, you can use the power rule for integration. For a power function of the form 'x^n', where n is any real number except -1, the integral is (x^(n+1))/(n+1) + C, where C is the constant of integration.

Question 3

3. Can you explain the concept of definite integrals?

Accepted Answer

Ans. Definite integrals are used to find the accumulated area under a curve between two specific points on the x-axis. It represents the net change in the quantity being integrated over a specific interval. The definite integral of a function f(x) from a to b is denoted as ∫[a to b] f(x) dx and can be evaluated using the fundamental theorem of calculus.

Question 4

4. What is the integral of a trigonometric function?

Accepted Answer

Ans. The integral of a trigonometric function depends on the specific trigonometric function and the limits of integration. For example, the integral of sine function (sin(x)) is -cos(x) + C, where C is the constant of integration. Similarly, the integral of cosine function (cos(x)) is sin(x) + C.

Question 5

5. How do you evaluate improper integrals?

Accepted Answer

Ans. Improper integrals are evaluated when one or both limits of integration are infinite or when the function being integrated is not defined at some point within the interval. To evaluate improper integrals, you either take the limit as a bound approaches infinity (or negative infinity) or break down the integral into two or more integrals using vertical asymptotes or points of discontinuity.

Integrals of Some Particular Functions Video Lecture - for SSS 3

Mathematics for SSS 3

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