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Proof: Integrals of some particular functions Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Proof: Integrals of some particular functions Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is the integral of a constant function? |  |
Ans. The integral of a constant function is equal to the product of the constant and the variable of integration. For example, the integral of the constant function f(x) = 5 is equal to 5x + C, where C is the constant of integration.
| 2. How do you find the integral of a polynomial function? | |
Ans. To find the integral of a polynomial function, you can use the power rule. For each term in the polynomial, increase the exponent by 1 and divide by the new exponent. For example, the integral of f(x) = 3x^2 + 2x + 1 would be (3/3)x^3 + (2/2)x^2 + x + C, where C is the constant of integration.
| 3. What is the integral of a trigonometric function? | |
Ans. The integral of a trigonometric function depends on the specific trigonometric function involved. For example, the integral of sin(x) is -cos(x) + C, where C is the constant of integration. Similarly, the integral of cos(x) is sin(x) + C.
| 4. Can the integral of a function be negative? | |
Ans. Yes, the integral of a function can be negative. The sign of the integral depends on the behavior of the function over the interval of integration. If the function is mostly below the x-axis, the integral will be negative. Conversely, if the function is mostly above the x-axis, the integral will be positive.
| 5. Is the constant of integration necessary when finding integrals? | |
Ans. Yes, the constant of integration is necessary when finding integrals. Since the derivative of a constant is always zero, the integral of a function will have infinitely many possible solutions. The constant of integration represents a family of functions that differ only by a constant value. Therefore, it is important to include the constant of integration when finding integrals.
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