1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

Q: Evaluating 9-x² dx using trigonometric substitution will lead to: A of th (A) cos²0d0 [*/ cos²0de Ⓒ…

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

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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: Evaluate the double integral: 2ydydx A 4 9 B) m 100 8 NIG 2 9 2

A: To find the value of given double integral.

Q: 1 3 x + x Solve the integral: S 6 ® ni.s.c A) 1+ x + C 6in|5+x²|+C B © h1+xel+c c) C Fin/1+ o D + x…

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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: In this question, we want to know the limits of the Integral as a horizontal element.

Q: f(x)=√3x-2 on the interval Let of the resulting solid. 83 (A) -unit 3 135 43x B -unit3 125 83x…

A: Ans : A

Q: Find the volume of the solid of revolution generated when the area described is rotated about the…

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Q: Given A B C D f(x) dx = 0 and 11 6 0 ¹² f(x) dx = 11 6 I 11 5 55 6 evaluate S²3f(x) dx - ₁2f(x)dx.…

A: we have to find the integral

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

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Q: If (x+1) dx (x+2)(x-1)² S -=S= A B + x + 2 + x-1 C (x-1)2 dx, the values of A & C respectively are:

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Q: Question 13 3 2 Evaluate the triple integral: f(x+y+z)dydxdz A) 24 B) 18 C) 6 D) 12

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Q: Evaluate the given definite integral [ 2x³ – 6x² dx, from x = 1 to x = 2 X²

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Q: cylinder cone pyramid if this triangle is rotated about the x axis, what figure is formed?

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

A: Find:when we can use power formula

Q: Question 33 If g(x)=- A) B D d = 2√²-1 (2 ·S^*^[e'-In(21+1)]dt, find g''(x) - 4 (2x+ (2x + 1)² e*…

A: Solved below.

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

A: To evaluate the integral. Option A is correct.

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

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Q: Evaluate the triple integral: A) 6 B) 18 C) 24 D) 12 3 2 1 ²³√ [²√ √ 0 (x+y+z)dydxdz

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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: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 2+In3 +C (3e)3+cosh2x B) 2+2ln3…

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Q: Evaluate the improper integral A) diverges 3 B 4 с N|9 2 3 -dx

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

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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: Stan² √I+1² 0 l+e' 1+tan²x tanx 1+e In (secx)√1+tan²x 1+et tanx sec²x 1+elanx sec 3x If f(x) = A B…

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

Q: Using shell method, find the volume of R, when it is bounded by y = x³, x = 0, y = 8 about x- axis.

A: Shell method

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: 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: Evaluate the improper integral 3 A 4 B) diverges с 0 D 2 N|O √√² 3³/3 m|f 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 D H|m -unit² 3 q…

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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: Determine which of the given differentials is/are exact. In case it is exact, find the functions of…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A: To find the volume of the solid.

Q: If 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: Evaluate the improper integral 3 -2 X -dx

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Q: 1 √√√√√x+x X Solve the integral: S- @ =√² m/1 + x ²³ / + c A C (1) 6in/5+ x ³²³| +C B © ²/³ m/1 + x…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x +1.

A: Correct option is A

Q: Transforming A B C D dx using miscellaneous substitution will yield to secx + 1 2-2z² -dz 1+z² z²+z…

A: Here, the given integral is: I=∫dxsec…

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

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Q: How many antiderivatives does a function of the form f(x)=x" have when n0? (A) none (B) may vary…

A: solution

Q: Let f(x)=√3x-2 on the interval axis and find the volume of the resulting solid. 43л -unit 3 135 83…

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Q: y = 5 tan x³ + sec(3x)

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Q: S D dx (x+1) log(x+1) In[log(x+1)] + C Evaluate: A In 10 ® -log B log² (x + 1) + C In 10…

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Q: Determine the area bounded by the functions f(x) = (x + 1)3³ and g(x)=x+1₁ A unit² B unit² 3 Ⓒunit²…

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Q: Question 16 d If g(x) = == S[e²-In (21+1) ]dt, find g(x). dx 4 A et + (2x+1)2 e* -In(2x+1) 4 e¹+ (2x…

A: We will first find g(x).

Q: Evaluate the improper integral 3 A 4 B) diverges C D —— 6/0 m|+ ² 0

A: Topic:- application of integration

Q: Question 33 Evaluate: :S₁ A B с D dx (x+1) log(x+1) -In[log(x+1)] +C In 10 -log² (x + 1) + C 2 -In…

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