Write the limit lim no 2 이 2 2-2 da; dx; da; dx; 3-2 32 3 512 102 5 2 Aæ as a definite integral over the interval [1,4], and evaluate it. xi

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

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Q: The volume of the solid generated by revolving the region bounded by x2= 4y and y2=4x about y=4 is…

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Q: Find the area bounded by the curve y = 1x³ - 2x² + 3x and the line x3_ 16 16 square units 10 square…

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Q: For the function y = (9x2 - 27)/x3 , determine the increasing and decreasing intervals, and identify…

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y = 4 is…

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Q: The integral B D a us can be transformed to which of the following using trigonometric substitution?…

A: Topic = Integration

Q: consider ∫ xsinx cox dx= f(x) sin2x - g(x) cos2x + C. what is the value of f(1) + g(1)

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Q: Evaluate [sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after…

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Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

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Q: Find the area bounded by the trigonometric curves 3.667 square units 2.828 square units 3.459 square…

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Q: [ sin(mx) cos(nx) dx- D Suppose m and n are constants and m #n. Evaluate 1 1 A -cos(m-n)x- =…

A: This question can be solved using the concept of integration of trigonometric functions.

Q: 3x5 ·S -dx- Using the method of partial fractions, the given integral can be written as 3x4+6x³3x² -…

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Q: QUESTION 12 x 1/2 ·S For S S- S- dx and using the substitution=x1/2, the resulting integral takes…

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Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)² A +…

A: Since you have asked multiple questions , we will solve first question for you. If you want any…

Q: y dy Find S- y+2 A ²/(√x+2-5)(-5√/y+2+y+21)+C ℗ ²/(√3+2-5) (5√/y+2-y+24) + C B Ⓒ(√x+2-5)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3x5 3x4+6x³-3x² - 6x B с -+ x-1 x+1 x+m S= Consider Sx-m+- A xm+-+- -dx. Using the method of partial…

A: Since the degree of the numerator is not less than degree of the denominator, perform polynomial…

Q: Evaluate A B Ⓒ D S= x² - 4x 2 x² - 4x 2 x2-2x 2 x²-2x-In 3x5 3x4+6x³3x² - 6x - (x-1) 1/6(x+2) 16/3…

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Q: Find the area bounded by the trigonometric curves y=sinx and 3.667 square units 3.459 square units…

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Q: Find the area bounded by the curve y=-x³ 16 (A) 8 square units B) 4 square units C) 16 square units…

A: Take the integral of the first curve minus the second curve.

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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Q: Question 17 1/2 S. dx and using the substitution = x 1/2, the resulting integral takes the form:…

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Q: The integral A B C D S³ x dx x² + √√√x²-1-1 sec²0 de 1+tano sine de 1 + cose sece tane de sece - 1…

A: We have to solve above integral

Q: For the function f(x) = 2x4 - 16x2 , find and identify any extrema (maximum/minimum) using the…

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Q: 3x5 Evaluate S 3x4+6x33x2 - 6x O x2−2x +In 2 x²-2x-In O x² - 4x 2 O x² - 4x 2 -dx, using method of…

A: Integration

Q: Evaluate Stan" (x) sec¹x dx 1 A m+1 I m+3 B 1 -tan (m + 1)(x) +- m-1 1 -tan (m + 3)(x) + m+1 -tan…

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Q: 1 3 Find the area bounded by the curve y== -x3. -x² + 3x and the line y=x. 16 10 square units 8…

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Q: Question 5 The integral - (Α S se ® / B Ⓒ / - (D x dx x²+√√√x²-1-1 *sec²0 de 1+tano sece tane de…

A: We have to find out

Q: QUESTION 18 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

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Q: Question 3 To evaluate A B D te fx-cost x²cosx dx use integration by parts. What is the expression…

A: The objective is to find the correct option.

Q: Consider and C. -dx Using the method of partial fractions, the given integral can be written as…

A: Here, 3x53x4+6x3-3x2-6x=x-m+Ax-1+Bx+1+Cx+mor, x4x3+2x2-x-2=x-m+Ax-1+Bx+1+Cx+mor,…

Q: π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=—. 4 4 (A)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3x5 3x4+6x33x² - 6x Evaluate A B (C) (D) ·S= x²-2x-In x² - 4x 2 x² - 4x 2 x² - 2x 2 + In + In + In…

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Q: 6 "Cosx dx. Sinx+25inx+5

A: Integration by Trigonometric substitution:

Q: Find the area bounded by the curve ya O 16 square units O 10 square units 4 square units O 8 square…

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Q: Question 13 The integral dx √(x²+4)² c'e ³0 do sin²0 de Ⓒ-csc³0 Ⓒos²0 csc ³0 de cos¹0 de can be…

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Q: y dy Find 13 using the substitution +5=√y+2. √y+2 A ²/ (√x+2-5) (5√/y+2-y+24) + C 3 B (√9+2-5)…

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Q: 11. The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4…

A: Follow the procedure given below.

Q: S- For x 1/2 U 4u U dx and using the substitution -du -du -du 4u 4- (21²) ² -du u=x1/2, the…

A: The objective is to find the correct option.

Q: dx The integral can be transformed to which of the following when trigonometric substitution is…

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Q: Evaluate tan" (x) secx dx. 1 A n(m + 1)(x). m+1 1 (В -tan (m + 2)(x) + m+2 1 -tan (m+1)(x). m+1 1…

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Q: Question 19 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

A: Let's find.

Q: sin (mx) cos(nx) dx

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Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: We have to find the radius of inner circle

Q: 3 3--x2+3x and the line y=x. 4 Find the area bounded by the curve y=-x³- 16 10 square units 16…

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Q: Evaluate tan" (x) sec¹x dx A B © D -tan (m+3)(x) + ¹ -tan (m+1)(x) + C m+3 m+1 −tan (m +1)(x) — —_¹…

A: This question can be solved using the concept of integration by substitution.

Q: Question 8 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

A: Solved below.

Q: Secor, x²cosx dx use integration by parts. What is the expression after the second integration by…

A: We have  to solve above integral

Q: The rate of growth of a population after t years is given by the equation P(t) = 5t. What is the net…

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Q: 19. The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4…

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Q: Find the area bounded by the trigonometric curves O2.828 square units 1.414 square units 3.667…

A: topic - area bounded by curves