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Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: Question 5 The improper integral +∞0 5+0⁰ 0 ex dx is

A: We can solve this as follows:

Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A:

Q: Question 37 1 Solve the integral: S- dx √√√√x+x A m/1+ + X +C ℗ 6n/5+x²³| +C B Ⓒ1+x²+c с X C =…

A:

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

A: We need to choose correct option.

Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u 9…

A:

Q: . Evaluate 1 4-x² dx

A:

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

A:

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

A: Here we have to determine the 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:

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

A:

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

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Q: Find the volume of R using shell method, when R is bounded by y = √x - 2, y = 0 and x = 4 about the…

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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…

A:

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: limit of integration

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

A:

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: If the Laplace transform of f(t) = e cos(et) + t sin(t) is determined the a. a shifting theorem can…

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

A: the point of intersection of  y=x-1 and y=(x-1)3  and y=0 are (0,-1),(1,0) and (2,1) the line…

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…

A:

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

A:

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

A: We have to choose correct option

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

A: We have to choose correct option

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: Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

A: To evaluate the integral.

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

A: Given g is a differentiable function and range of g is on the interval I and  F is antiderivative of…

Q: Which of the following can be determined O [ars) A (4f(x) + 9h(x) dx B [²³(f(x) + g(x) (f(x) + g(x)…

A: We have to find out

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

A:

Q: 1 X + X Solve the integral: Gin|5+x²|+C A 5 @ B {/in/1+x³²|+c C © =√³ m/₁ + x ²³ / + C 6 ©…

A:

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

A:

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

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Q: Determine the area bounded by f(x) = x² − × a axis. A - unit² B unit² C unit² 2 -unit? +|5

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

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Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

Q: 1 Solve the integral: J 3 x + x 5 6 x In|1+ A +C + C Shi+x+c 6 1+ C 5 1+x8 +c +C B C 516 In|1+ - dx

A:

Q: q13

A: We have to calculate the given indefinite integral

Q: 14. Evaluate [4³x dx 3x O 4³x 3x +C 6ln2 O 4³x In4 O 43x+1 3x+1 +C O None of these +C

A:

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

A: We have to choose correct option

Q: (x+1)dx (x+2)(x-1)² 2 . 93 15 S If (A (B) (c) D -- 9 9 9 2/3 W|N 3 A = -√ [14/2₂ B + x+2 x-1 +…

A:

Q: Question 23 en [ "_f(x)dx=0 and ["f(x)dx = 1, evaluate Given A 0 B (u) D 11 76 55 =¹3f(x) dx -…

A: We have to find out the integral

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

A: Topic:- application of integration

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: Question 14 dx Transforming S using miscellaneous substitution will yield to secx + 1 Ⓒ √ 1 + 2 ²2/0…

A:

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

A:

Q: How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B) none may vary…

A:

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

A:

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: (x+1)dx (x+2)(x-1)² S A 2 - x+2 B -1 + (x-1)2 ]dx. the values of A & C respectively are:

A: integration