1 11 Given 1 [²_f(x) dx = 0 and [ f(x) dx = 1 1 ₁ ¹3f(x) dx - 2f(x)dx. evaluate 6 0 -1 55 A 6 11 B 5 11 C 6 D 0

Q: If f (x) = A (В B C D Stams. 0 sec²x tanx 1+1² Ite¹ 1+e tanx sec ³x 1+e -dt, then f'(x) equals tanx…

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

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

A: A detailed solution is given below.

Q: How many antiderivatives does a function of the form f(x)=x" have when n*0= A) infinitely many (B)…

A: We have to choose option find antiderivative

Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

Q: Evaluating √√9-x² dx using trigonometric substitution will lead to: 57/2 A 18 "/2 cos²0d0 35*1/2 B…

A: ANS: B

Q: To evaluate the integral [ sin³@cos³0d0 by trigonometric transformation, we use the identity; 1 +…

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Q: x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the…

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Q: πT Evaluate the integral: sin(3x)cos(3x) dx រ 1 A 3 (B) i D 1 براس 1

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Q: Determine the area bounded by f(x)=x²-x and x-axis. A unit² -unit2 unit² |+ B 2 © ½ u Ⓒ / unit ² D…

A: Let's find area of given curve.

Q: Given f(x)dx =0 and f²f(x)dx = 끝. 11 A 6 55 B 6 11 C 5 D evaluate S" 3f(x)dx - [2f(x)dx.

A: Here, given that: ∫-11f(x) dx=0, ∫01f(x) dx=116

Q: the 2) Find the standard deviation of sample. population 2, 4, 7, 12, 15 Find the variance for the…

A: We have to find the variance and standard deviation.

Q: Question 32 Solve the integral: A) 3√√√x² +C (B) ex 3 2√x² +C с D 6√√x +C 3√x x² dx

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

A: Topic:- calculus

Q: Question 21 dx Evaluate: S (x+1) log(x+1) (A) In 10 log² (x + 1) + C 2 B In[log(x+1)] +C In 10 C…

A: We need to evaluate integral.

Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 A -dz 1+z² B 1² 2-2z² 1+z²…

A: Given problem:-

Q: Question 14 If [ _ ( x + 1) dx S A B C D (x+2)(x-1)² 2 . 93 -io 1 6.11 1 -- - 9 9 2 - - 3 - 3 2 - 3…

A: To find the value of A and C  in the given integral.

Q: 15 S A B (c) D (x+1)dx (x+2)(x-1)² 1 2 -- 9 1 2 " 9 3 -lo 1 9 " - - W|N 2 1 9 3 W|N 3 -S[₂ = A B +…

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

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Q: Evaluate the double integral: A 9 2 5 2 (В с D m|w 416 5² 5²² 2ydydx

A: A detailed solution is given below.

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

A: To find integrand the steps are as follows.

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

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Q: S √√9-x² dx using trigonometric substitution will lead to: **/2 cos²0d0 Evaluating Ⓒ 18/² A 95*1/2 B…

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Q: Question 12 Given S (A) (-∞0,00) B (1,00) D -dx, determine all value/values of P for which the…

A: Here we have to determine all values of p of the given improper integral in which the integral is…

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

A: Please follow the next step.

Q: Find the volume of solid generated by revolving the region bounded by g(x)=x²+2x+ 5about the x-axis.…

A: Given:      fx=x2+1      gx=-x2+2x+5  Volume of solid revolving around the region is…

Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

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Q: e the integral: S- 1 √x © $ n/²+x²³/+c +C © ²0/₁+x²³²/+c\ +C == n/₂+x²³/+c +C √x+x dx

A:

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

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Q: Question 9 Which of the following represents the volume of the solid generated by revolving the…

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Q: $²² Α) (1,∞0) B (-∞,1] (-∞0,00) Given D {0,1} dx, determine all value/values of P for which the…

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Q: Question 26 Determine the integral: x²cosxdx A x²sinx-2xcosx +2sinx + C B x²sinx + 2xcosx-2sinx + C…

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Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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Q: Question 2 Solve the integral: A √√x 3 B 33√/ x² +C 3√x² +C 6 6√√x +C D √√ 3√x dx

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Q: y 3 Arcsec 3x

A: Find out the y'.

Q: Solve the integral: √x 3 / x2 + C 6 6/x + C 33.2 + A B (C) D + C dx

A: On solving this we will get Option (C) is correct

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.

Q: (x+1) dx (x+2)(x-1)² 2 3 If 15 S. A B (C) D -10 2 . 9 3 W|N I 93 9 —— 3 =1[₂ = A x + + B x-1 +…

A: See the details solution in below

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

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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: 2+3x-7) X-2 dx Evaluate the integral: Se A²+ +In|3x-6|+C Ⓡ 1/²/₁ 2²+5x+! In/x-21 +C B 3 x²+5x+In…

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Q: S Given dx, determine all value/values of P for which the improper inte хр A (-∞,1] B {0,1} C…

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Q: +∞o fthe 0 The improper integral edx is

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

A: Conic method

Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² − 4 = 0, using a vertical element.…

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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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