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Application of Integral Class 12 Notes Maths Chapter 8

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FAQs on Application of Integral Class 12 Notes Maths Chapter 8

1. What are some real-life applications of integrals?
Ans. Some real-life applications of integrals include calculating the area under a curve, finding the volume of irregular shapes, determining the average value of a function, calculating work done by a variable force, and finding the center of mass of an object.
2. How can integrals be used to find the area under a curve?
Ans. Integrals can be used to find the area under a curve by taking the definite integral of the function within a given interval. The integral represents the accumulation of infinitely small areas under the curve, resulting in the total area enclosed by the curve and the x-axis within the specified interval.
3. How are integrals used to calculate the volume of irregular shapes?
Ans. Integrals can be used to calculate the volume of irregular shapes by taking the definite integral of the cross-sectional area function along the axis of revolution. By integrating the cross-sectional areas from the starting point to the endpoint, the total volume of the irregular shape can be determined.
4. How can integrals be used to determine the average value of a function?
Ans. Integrals can be used to determine the average value of a function by taking the definite integral of the function over a given interval and dividing it by the width of the interval. This calculation represents the average value of the function over that interval.
5. In what ways can integrals be used to calculate the work done by a variable force?
Ans. Integrals can be used to calculate the work done by a variable force by integrating the product of the force function and the displacement function over a given interval. This integral represents the accumulation of infinitesimal work done by the force and provides the total work done.
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