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Applications of the Definite Integral PPT Maths Class 11
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Page 1 For finding … 1. V olumes, 2. Lengths of plane curves, 3. Centers of mass, 4. Areas of surfaces of revolution, 5. Work, and 6. Fluid forces against planar walls. Page 2 For finding … 1. V olumes, 2. Lengths of plane curves, 3. Centers of mass, 4. Areas of surfaces of revolution, 5. Work, and 6. Fluid forces against planar walls. Page 3 For finding … 1. V olumes, 2. Lengths of plane curves, 3. Centers of mass, 4. Areas of surfaces of revolution, 5. Work, and 6. Fluid forces against planar walls. Page 4 For finding … 1. V olumes, 2. Lengths of plane curves, 3. Centers of mass, 4. Areas of surfaces of revolution, 5. Work, and 6. Fluid forces against planar walls. Page 5 For finding … 1. V olumes, 2. Lengths of plane curves, 3. Centers of mass, 4. Areas of surfaces of revolution, 5. Work, and 6. Fluid forces against planar walls.Read More
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FAQs on Applications of the Definite Integral PPT Maths Class 11
| 1. What is the definite integral? |  |
Ans. The definite integral is a mathematical concept that represents the area under a curve between two specified points on a graph. It is denoted by ∫(lower limit to upper limit) f(x) dx, where f(x) is the function and dx represents an infinitesimally small change in x.
| 2. How is the definite integral used in real-life applications? | |
Ans. The definite integral has various applications in real-life scenarios. It can be used to find the area of irregular shapes, calculate the total distance traveled by an object with varying speed, determine the total accumulation of a quantity over time, and analyze population growth or decay.
| 3. Can the definite integral be used to solve optimization problems? | |
Ans. Yes, the definite integral is often used to solve optimization problems. By finding the maximum or minimum value of a function within a given interval, the definite integral helps in determining the optimal solution to problems involving cost, profit, time, or any other measurable variable.
| 4. How does the definite integral relate to the fundamental theorem of calculus? | |
Ans. The fundamental theorem of calculus establishes a connection between differentiation and integration. It states that if a function F(x) is the antiderivative of f(x), then ∫(a to b) f(x) dx = F(b) - F(a). This theorem allows us to evaluate definite integrals by finding the antiderivative of the integrand and applying the limits of integration.
| 5. What are some common techniques to evaluate definite integrals? | |
Ans. There are several techniques to evaluate definite integrals, including the use of antiderivatives, substitution, integration by parts, partial fractions, and trigonometric identities. The choice of technique depends on the complexity of the integrand and the available tools for simplification.
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