Definite Integrals (area under a curve) (part III)

# Definite Integrals (area under a curve) (part III) Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Definite Integrals (area under a curve) (part III) Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is a definite integral?
Ans. A definite integral is a mathematical concept used to calculate the area under a curve between two specified points. It represents the limit of a sum of areas of rectangles as the width of the rectangles approaches zero.
 2. How is the area under a curve calculated using definite integrals?
Ans. The area under a curve can be calculated using definite integrals by evaluating the integral of the function over a given interval. This involves finding the antiderivative of the function and then subtracting the value of the antiderivative at the lower bound from the value at the upper bound.
 3. Can definite integrals be negative?
Ans. Yes, definite integrals can be negative. The sign of the definite integral depends on the shape of the curve and the interval over which the integral is evaluated. If the curve lies below the x-axis in certain regions, the area under the curve will be negative.
 4. What are some real-life applications of definite integrals?
Ans. Definite integrals have numerous real-life applications, including calculating the total distance traveled by an object given its velocity function, determining the total revenue or cost of a business over a specific period, finding the average value of a function over a given interval, and finding the center of mass of an object.
 5. How can definite integrals be used to find the length of a curve?
Ans. Definite integrals can be used to find the length of a curve by considering small sections of the curve as straight lines. By approximating the curve with these straight lines and summing up their lengths, the total length of the curve can be obtained. This process is known as arc length integration.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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