Definite Integral Calculus Examples, Integration – Basic Introduction, Practice Problems
Definite Integral Calculus Examples, Integration – Basic Introduction, Practice Problems

Question

Question 2: Evaluate the following integral. a) b) Evaluate over the area of cardioid above the initial line. Question 3: Evaluate the integration by Changingof order of integration of . Question 4(a): By Double integral show that the area between the parabolas and is .

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Question 2

Example 7. Find the entire length of the curve . Sol. The equation of the curve is

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Question 3

A certain sum at sim years. Find the sum. months. Ans, Rs. 2,8001 A certain sum and its interest th of the principal, find princip 4 years become Rs. 480 . If interest is [Ans. Rs. ] A trader bgrrows Rs. from a moneylender and a bank. If the rate of interest are per annum and per annum respectively and the trader had paid Rs. 16,600 as interest for one year, find the sum borrowed from the moneylender and bank. [Ans. Sum borrowed from moneylender Rs. 30,000 Sum borrowed from bank Rs. 70,0001 5. Divide Rs. 2,708 , between Hari and Shyam so that Hari’s share at the end of 5th year is equal to Shyam’s share at the end of 7th year at the rate or per annum. [Ans. Hari’s share Rs. 1,580 and Shyam’s share Rs. 1.128 ]

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Question 4

Consider a binary operation *on , set of natural numbers, defined by . Choose the correct answer (a) * is both associative and commutative b) * is commutative but not associative (c) * is associative but not commutative d) * is neither associative not commutative 14. Let be a binary operation defined on . Find which of the following binary operations are associative. (a) (b) (c) (d) 15. Let be a binary operation defined on . Find which of the following binary operations are commutative. (a) (b) (c) (d) . ANSWERS

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 Question Text Question 2: Evaluate the following integral. a) b) Evaluate over the area of cardioid above the initial line. Question 3: Evaluate the integration by Changingof order of integration of . Question 4(a): By Double integral show that the area between the parabolas and is . Updated On Feb 19, 2023 Topic Integration Subject Mathematics Class Class 12 Passed Answer Type Video solution: 2 Upvotes 234 Avg. Video Duration 11 min

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