Find the volume of solid generated by revolving the region bounded by f(x)=x²+1and g(x)=x²+2x+5about the x-axis. 37x unit B 63x unit3 Ⓒ72x unit ³ 56x unit 3

Q: +3x-4)³ Solve the integral: Seln(2x²+3 (4x+3)dx eln(2x²+3x- 3x-4)³ A (2x²+3x-4) (2x²+3x+4)4 B + C 4…

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Q: √²² (3x² +9y²) dxdy Evaluate the double integral: (A) 40 (B) 80 Ⓒ30 (D) 60

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Q: X √√/31/22 Solve the integral: 3√/x² A + C 6 B 6√√√x + C C3√√√x² + C C) dx

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Q: Solve the int B ²+3x-4)³ (4x+3)dx integral: Seln (2x² + 3 eln(2x²+3x-4)³ + C (2x²+3x-4) (-4)³² (4x +…

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Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

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Q: The improper integral (A) e B) 0 с 00 D 1 8 0 edx

A: ∫0∞e-xdxSubstitute u=-x→dudx=-1→du=-dx=∫-e-x

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: We can solve this as follows:

Q: Evaluate the double integral: A B C D m|m NIG 2 2ydydx

A: You must have an idea of double integration to solve this problem. Option D is the right choice. The…

Q: Find the volume of the solid generated using washer method by revolving the region bounded b y = x²…

A: Let's find volume of solid by using washer method.

Q: Evaluate the integral: Se³+ A B C 3+cosh2x33+cosh2x sinh2x dx (3e)3+cosh2x + C 2+2ln3 (3e)3+ sinh2x…

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Q: hich of the following represents the volume of the solid generated by revolving the region bounded…

A: Let's find volume of two curves rotating about x axis.

Q: Evaluating A 18 √*1/200 (A) **/2 B √9-x² dx using trigonometric substitution will lead to: cos²0d0 0…

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Q: Which of the following can be determined given f(x)dx=5, g(x)dx=7, and and T h(x) dx = -5

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Q: After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the…

A: answer is in next step

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

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Q: 11 Given ~ [²₁_f(x) dx = 0 and [ ² f(x) dx = 1 1 1 4 11 A 6 B C 0 55 0 evaluate • [²³f(x) dx - ²₁²…

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Q: In the indefinite Integral in(cosh x + ex)- A sinh x + ex In(cosh x + sinh x tex cosh x + ex In(cosh…

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Q: Question Evaluate the indefinite integral given below. Provide your answer below: -5x²sec²(3x³) tan³…

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Q: √ √9-x S*/2 (B 9 ft/cos Ⓒ 18 "/2 D 95*1/2 sin Evaluating A 18 9-x² dx using trigonometric…

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Q: 1 m ( x² + 3102=²7) dx x²+3x-7 X-2 Evaluate the integral: Se A +2²2 + — + In|3x-6√ + C Ⓡ X/²2 ₁ B…

A: A detailed solution is given below.

Q: If a horizontal element is used to find the area bounded by y=√x, x=4 and the x-axis, the limits of…

A: Integration

Q: 8. Graph the rational function. horizontal asymptotes. 3x-12 a. r(x)= x+1 Show clearly all x- and…

A: Graphs are to be drawn first and then asymptotes and intercepts need to be marked.

Q: Which of the following is NOT a method for finding volume of solids of revolution? A) washer method…

A: Conic method

Q: 2. Find an equation for the plane that passes through the points P = (2,-1,3), Q = (0,0,5) and…

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Q: dx (x+1) log(x+1) 1 In[log(x+1)]+C In 10 -In 10 log² (x + 1) + C 2 In 10 In[log(x+1)] + C -aluate: A…

A: Topic:- application of integration

Q: Given Sf(x) dx = 0 and √ ² f(x) dx = 11 6 " 1 0 •√3f(x) dx - √₁2f(x) dx. evaluate

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Q: The part of the plane 2x 5y + z = 10 that lies above the triangle with vertices (0, 0), (0, 6), and…

A: Double integration need to be done.

Q: Find the gradient vector field of f. f(x, y, z) = 2√x² + y² + z²

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Q: In 1991, there were 41,144 shopping centers in a certain country. In 2001, there were 48,157. (a)…

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Q: 10–f()=e" .sinh |2t. e-³¹ sin 2t -31 12- f(t) = t 14-f(t)=t² cos Zt. 16-f(t)=t² sin wt. = {0…

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Q: Which of the following can be determined given 3 3 [ f(x)dx=5₁ g(x)dx=7, and √ √h(x) dx = -5 3 A √…

A: See the details solution in below

Q: хра (q

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Q: 9. For what value of k, k> 0, does (4kx-5k) dx = k² O 1 O 2 3 O 4

A: On solving this we will get

Q: y 3 Arcsec 3x

A: Find out the y'.

Q: X √√x dx Solve the integral: (A) 3 B + C 6 с 6√√x +C D 3√√√x² +C

A: To integrate the following problem

Q: -21 1 (1 + 3x)2 dx

A:

Q: Which of the following can be determined given f(x) dx = 5₁ x) dx = 5,₁ ₁ g(x)dx=7, and h(x) dx = -5

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Q: Determine the area bounded by f(x)=x²-x and x-axis. A unit² ® unit² Ⓒunit² 1 D unit²

A: topic - area bounded by curves

Q: dx 15 √(x+2)(x-1)²² -S[ +42 + (A) 93 B (C) (D) 12 93 —— . 2 3 2 3 B x-1 + (x −1)² ]dts dx, the…

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Q: Solve the integral: A B D 3√√√x² +C 6√x +C + C 6 √x 3 3√x dx

A: We have to solve integral

Q: Solve the integral

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Q: Evaluate the double integral: (A) 40 B 30 C) 60 D) 80 ²(3x² +9y²) dxdy

A: The integration are.  .

Q: Let f(x)=√3x-2 on the interval. 1] Revolve the region between the curve, y=1 and y-axis about the…

A: Here is the solution of the given problem. We solve this by using shell method

Q: - 1₁₂ (3+√4-2²³) dx -2

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Q: 17. Evaluate [9e³x dx O9e³c+1 3c+1 O9e3c O9ec-3 3e³c-3

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Q: d [e'- In (21+1)]dt, find g(x) . dx -2 A ex-In(2x+1) 2 B ex_ (2x + 1)2 4 C (2x + 1)² 4 D (2x + 1)²…

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Q: Determine the area of the region bounded by 3x - 5y + 4 = 0 and y-axis from y = 2 to y = 5.

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Q: f f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

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Q: Find the area bounded by : f(x)=e*, g(x) = e¯* and x = 3. A (e²-1)² e2 sq. units (e²+ 1)² e2 (e³-1)²…

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Q: 3. Use two rectangles of equal width to estimate the area between the graph of f(x) = x + cos(x) and…

A: Solved below.