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

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

A: Given that g be a differentiable function and the range of g be an interval I.  f is a function…

Q: the integral: (u +3) du 1²5 -dx (3) √74³ cscxcotxdx

A: We have to find out integral

Q: Transforming S Ⓒ / ² A 1-z² 1+z² ® / 12-2 B 1+z² © Ⓒ S ²¹²+² dz 1-z2 1+z² D S 1-z² dx secx + 1 -dz -…

A:

Q: 15+0. The improper integral e* dx is

A:

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

A: The integration are

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

A: Solution: Natural length  = 3 ft   ---> 18 ft-lb 3 ft to 6 ft

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

A:

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

A: We can solve this as follows:

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

A: Solved below.

Q: 1 Solve the integral: S dx 3 x ที่ X + X h_1+x+c A C Ⓡ 6ın|5+x=³² | +C B © h1+x8 l+c + C h1+x+c D +…

A: Given that we need to solve the following  integral.

Q: alculate the amplitude and period of the function: f(x) = 3 sin(a) - 1 O Amplitude: 1, period: 2.…

A: Given query is to find the amplitude and the period of the function.

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: We will have to find  qrea bounded by rhe curve  y= x1/2  X=4 and xaixs

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

A:

Q: - 1₁₂ (3+√4-2²³) dx -2

A:

Q: What is the instantaneous rate of change of y=√√zat z=2? 0 ม O - O none of the above 0

A: The function is given by y = x To evaluate: The instantaneous rate of change of the function at x=2.

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

A:

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

A: The region bounded by line y = x - 1 and the curve y = (x - 1)3 is as below

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: Find the slope of the line tangent to 2xy + π sin y = 2π through the point (1, π/2).

A: The slope of the line tangent to 2xy+πsin y=2π through the point 1,π2.

Q: Solve the integral: A 5n/1+x²|+C 5 (B) 6in 5+x' 6In|5+ +C 음 m/1+x²|+c C ³√|+C 1+x √√√√x+x² dx D

A:

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

A:

Q: antiderivatives does a function of the form f(x)=x" have when n*O? may vary depending on n How many…

A: Formula: Antiderivative of xn = xn+1/n+1

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

A:

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

A:

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

A:

Q: When calculating the integral shown, using trigonometric substitution method with 6x sen(B) = in the…

A:

Q: Find and sketch the domain of the function. f(x,y)=√y-x-8 Find the domain of the function. Express…

A:

Q: f(x) = Jax+b (2x²-1 if x < 2 if2 ≤ x

A:

Q: tanx f f(x) = = [tion. A B C √1+1² 1+e' In (secx)√1+tan²x tanx 1+e sec²x 1+ e tanx sec ³x tanx 1+e…

A: Integration

Q: Consider the vector field. F(x, y, z) = (9ex sin(y), 2e sin(z), 4e² sin(x)) (a) Find the curl of the…

A:

Q: Question Find the average value of f(x) = -3 cot (x) csc (x) + 1 over the interval [3 Submit an…

A:

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

A: Topic:- application of integration

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: Evaluating √9-x² dx using trigonometric substitution will lead to: -3

A:

Q: (2) secxtanxdx e definite integral by substitution: -21 1- (2) dx (3) [x√x-2dx

A: We have to find the value of the given definite integral according to the given information

Q: e: Sz dx (x+1) log(x+1)

A:

Q: Solve the integral

A:

Q: (1) ₂ (3+√4-x²) dx -2

A:

Q: Where is f(a) not continuous? JAROMEN M 0 :-2 SE 4 O 0 02 O nowhere O-2 and 2 O-2 0 2

A: here in graph we see that function is not contineous at 2 and -2 value there is not contineous graph…

Q: Solve the integral: A 3√√x² B + C 6 C 6√√x + C с D 3³√√x² +C ကြ Sv √√√x 3√x X dx

A:

Q: Question 9 d If g(x) = ·S*^[e'− In(2t+1)]dt, find g''(x) . dx -2 4 A (2x + 1)2 4 B (2x + 1)²…

A: Using leibnitz rule.

Q: (1) [ Evaluate the indefinite integral by substitution: a+bx² dx 3ax+bx3 (2) / sec³xtanxdx T

A:

Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; 1-cos20…

A:

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

A:

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

A: To find the work done.

Q: (2x³ + 5x-4) dx

A: Solved below.

Q: x³-8 4 x+2 x 16 2. lim

A:

Q: Verify that 2²4 ахду 22+ ду ах - for f(x, y) = 2x³y6 - 4x5y4.

A:

Q: Find the slope of the line if it is defined Through (-6,-7) and (-1,12) Select the correct choice…

A: Given query is to find the slope of the line.