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Integration.. - Class 12 PDF Download
The integral of the function 
w.r.t. x is:a)
, where c is a constant of integrationb)
, where c is a constant of integrationc)
, where c is a constant of integrationd)
, where c is a constant of integrationCorrect answer is option 'D'. Can you explain this answer?
Ref: https://edurev.in/question/481147/The-integral-of-the-function-w-r-t-x-isa-where-c-is-a-constant-of-integrationb-where-c-is-a-con
i applied the frmula and solved...but i dont find any option which tallies...if i did any mistake plz inform me...
FAQs on Integration.. - Class 12
| 1. What is integration and why is it important in calculus? |  |
Ans. Integration is a fundamental concept in calculus that involves finding the area under a curve or the accumulation of quantities over a given interval. It is important because it helps us solve problems involving rates of change, such as finding the displacement, velocity, or total distance traveled by an object.
| 2. How is integration different from differentiation? | |
Ans. Differentiation and integration are two fundamental operations in calculus. Differentiation calculates the rate of change of a function, while integration calculates the accumulation of a function over a given interval. In simple terms, differentiation finds the slope of a curve, while integration finds the area under a curve.
| 3. What are the different methods of integration? | |
Ans. There are several methods of integration, including:
- Direct integration: This method involves applying basic integration rules, such as the power rule, product rule, or chain rule, to find the antiderivative of a function.
- Integration by substitution: This method involves substituting a variable with another variable or expression to simplify the integral.
- Integration by parts: This method is based on the product rule of differentiation and helps to integrate the product of two functions.
- Partial fractions: This method is used to break down a complicated fraction into simpler fractions, which can be integrated individually.
| 4. Can integration be used to find the area of irregular shapes? | |
Ans. Yes, integration can be used to find the area of irregular shapes. By representing the irregular shape as a mathematical function, we can integrate the function over a specific interval to find the area under the curve. This is often done using definite integration, where the bounds of integration define the interval over which the area is calculated.
| 5. What are some real-life applications of integration? | |
Ans. Integration has numerous real-life applications, including:
- Physics: Integration is used to calculate the work done by a force, the potential energy of an object, and the motion of particles.
- Economics: Integration is used to determine the total revenue, total cost, and profit in economics.
- Engineering: Integration is used to calculate the area moment of inertia, the centroid of a shape, and the deflection of structures.
- Probability and statistics: Integration is used to calculate the probability density function and cumulative distribution function in statistics.
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Jan 05, 2025
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Document Description: Integration.. for Class 12 2025 is part of Class 12 preparation. The notes and questions for Integration.. have been prepared according to the Class 12 exam syllabus. Information about Integration.. covers topics like and Integration.. Example, for Class 12 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Integration...
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