2. Find the area under the curve y = x² from x = 0 to x = 3. -y-x² (1,1) x-1 (3,9) x-3

Q: e the triple integral: (x+y+z)dydxdz 6 24 18 12

A: Topic :- application of integration

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

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Q: Find the are bounded by the curve y = x and y = x^2 - 2. * 2/9 sq unit 9/2 sq. units 16/3 sq. units…

A: Use the intersection of the curve and then integrate the upper curve minuses the lower curve to find…

Q: 3 2 1 Evaluate the triple integral: S (x+y+z)dydxdz (A) 12 B) 18 24 (D) 6

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Q: 1 x + × olve the integral: 5 ® shi+x+c A C 5 6 ® $h1+x+c B C © 6n|5+x²|+c C D Shi+x+c C dx

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Q: aluate the integral [ sin³0cosº0d0 by trigonometric transformation, we use the identity; 1+ cos20…

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming Ⓒ S A 1-z² B 1+z² © √ 1 +…

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Q: Given the integral sec6 (x - 1) tan4 (x - 1)dx, which of the following equatio useful for…

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Q: How many antiderivatives does a function of the form f(x) = x^ have when n=0? A may vary depending…

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

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Q: Given √ 1 pdx.c A (-∞,1] B (1,00⁰) Ⓒ (-∞0,00) D (0,1) dx, determine all value/values of P for which…

A: This can be solved as follows:

Q: X √√√3/2 x² Solve the integral: A 6√√x +C 3√√x² (B - + C 6 Ⓒ3√√√x² +C с √x (D 3 dx

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Q: S Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: (x2y3 - 1+) dx + x3y2dy = 0 1+9x2

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

Q: If f (x) = A) B (C) D tanx √1+1² 1+e' 0 1+tan²x tanx 1+e sec ³x -dt, then f'(x) equals tanx 1 + e In…

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Q: If f(x) = A B C D tanx S 0 sec²x √1+1² 1+e¹ -dt, then f'(x) equals 1+e tanx In (secx)√1+tan²x 1+ e…

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

A: Here we have to find the integral for finding the volume.

Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

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Q: That statement "We can use the General Power Formula of Integration for indefinite integrals…

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Q: X lim x→1 x-1 Your answer x In x

A: Let's evaluate given function by using l'hospital's rule.

Q: etermine the area bounded by f(x)=x²-x and x-axis. 1 A unit² 2 B unit² 1 unit² 1 unit² D

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Q: •+∞0 The improper integral * fe 0 A) 0 B e C (D) 1 ∞ ex dx is

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Q: Question We can apply General Power Formula of Integration on which of the following integrals? A…

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

Q: Question 18 Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+…

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Q: Question 19 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

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Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

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

A: According to the properties of definite integral(A) ∫abkf(x)dx=k∫abf(x)dx      True(B)∫abkdx=k…

Q: Solve the integral: Seln(2x² + 3x−4)³ (4x + 3)dx

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1 A unit2 B unit² unit² Ⓒ /…

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Q: Which expression is equivalent to O cotx+sec x O cos x + cot a Otan x+sec x O sinx+tan x an £ ? cos…

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Q: 16. Evaluate O 1 O 2 3 O 4 8 X ²+36 dx

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Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

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

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Q: Determine the integral: x²cosxdx A x²sinx+2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C Cx²sinx +…

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Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

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Q: What kind of the polar graph has the equation r = 2 + 2 cos 0? limacon cardioid lemniscate…

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Q: etermine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x + 1 3 (A 1 (B) 1 unit² unit²…

A: To find the area bounded by curves

Q: In the indefinite Integral in(cosh x + e*)- A In(cosh x + e*) B) sinh x + ex D In(cosh x + e*) sinh…

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Q: =√x, x=4 and the x-axis, the limits of integration are: If a horizontal element is used to find the…

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Q: Given the integral sec (x - 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: Let's find useful formula for evaluation of integration.

Q: (D) 1

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Q: If g (x) = — _ _[e¹ — ln(2t+1)]dt, find g''(x) dx -2 (A) B C) D 4 et + (2x + 1)2 4 et + (2x+1)2 e* -…

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Q: Question 11 Let g be a differentiable function, and let the range of g be an interval 1. Suppose…

A: The integration are...

Q: Use the formula for the sum of the first n terms of a geometric sequence to find the sum of the…

A: Given that the geometric sequence is 7,14,28,56,112,....

Q: 19 Let u(x) = sin(x) and v(x) = x¹9 and f(x) = u'(x) = v'(x) = u'v - uv' f' 2² u(x) v(x)

A: sin(x)' = cos(x) dxndx=n.xn-1

Q: Determine the area bounded by f(x) = x² — X and x-axis. 1 A -unit² B -unit² Ⓒunit² 2 Ⓒ -unit² 1

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Q: Which of the following can be determined given ^ (A) [²(f(x) = g(x) dx ℗ ₁²³(f(x) + g(x) + h(x)) dx…

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Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3.

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

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Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration