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

Q: D sec²u=1+tan²u

A:

Q: (x+1) dx (x+2)(x-1)² = √ [+²2 S₁ B + - - 1 + x-1 (x-1)2 ]dx. the values of A & C respectively are:

A:

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

A:

Q: y = x Arccsc (+)

A:

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: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

A: We need to find volume.

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

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. 2 A 3/3/14 unit² ® 1/1/¹4 B unit² 1 (C) unit² D…

A: The area bounded by fx=x2-x and x-axis

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

A:

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

A:

Q: Which of these expressions represents the area bounded by y = 1/2 x^2 and y = 3x? * 6x + x²dx 6x…

A: To solve the following problem

Q: van [ f(x)dx = 5, [_o(x)dx=7, and [_n(x) dx = - -5 Which of the following can be determined given…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

A:

Q: Determine the integral: x²cosxdx (Α x²sinx-2xcosx-2sinx + C x²sinx + 2xcosx+2sinx + C x²sinx-2xcosx…

A:

Q: 4 Evaluate the double integral: 2ydydx 1 A B (ⒸⒸC) D m 100 8 +10 9 2 5 2

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

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

A: Please see the below picture for detailed solution.

Q: Evaluate the double integral: 2 √ ² √² (3x² +9y²) dx dy 0

A: To solve the given double integral.

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: Integration

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

A: We have to choose correct option

Q: If (A) (В (D (x + 1) dx (x+2)(x-1)² -ja دا | در 93 1 —— 9 9 . 3 2 3 x + 2 ++ x-1 (x-1)2 dx, the…

A:

Q: Evaluate the double integral: A B NIG 5 3 m|p 99 In +10 2ydydx

A: To solve the following double integral

Q: 0.06x, solve f'(x) = 130. (Round answer to nearest tenth.) Given f(x) = 250 e X =

A:

Q: Find d2y/dx2 for y2 + 2y = 2x + 1

A:

Q: Graph cach function using radians. 2. 1 - sin 29 - 1 2 0 0 0 یا

A: Please see the below picture for detailed solution.

Q: X-2 Se Evaluate the integral: (+3x-7) dx A x²+5x+In 3x-6|+C B +In|3x-6|+C C + In/x-21 +C 3 D)…

A: Solution:

Q: y = 2 sin 3x 1+3cos2x

A: We can solve this as follows:

Q: Question 14 dx Transforming - using miscellaneous substitution will yield to secx + 1 1-z² A 1+z²…

A: Here we have to transform the given integral by using miscellaneous substitution.

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 +…

A:

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

A:

Q: Determine the case of the following proper rational function after simplification: x + 2…

A: We have to find out simplification

Q: S 1 Solve the integral: √√√X = n/1+x²³²|+c A C {/in/1+x²³ | +c B © 6n/5+x²³²|+c C in/1+x³| +c D X +…

A:

Q: 1 S dx 3 x + x Solve the integral: 5 A + x +C 1+x+c n 1+x+c in 1 B + x + C © 6/5+x²³/+c C ® 1+x+c In…

A:

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

A: Substitute sec^2u=1+tan^2u B option is correct.

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: The limits of integration will be the interval on the x-axis for which the area is bounded.

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: 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…

A:

Q: A bullet is fired with muzzle velocity of 150 m/s at an angle of elevation = 45°. Gravity = 9.8…

A: Since you have posted a question having multiple sub part as per guidelines we can solve only first…

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: Evaluate the integral: 1 A 6 B С 3 D HIM P 16 sin(3x)cos(3x) dx

A: Solve by integration

Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

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

A:

Q: If (x+1) dx (x+2)(x-1)² 1 93 2 93 S- A B D -io 1 W|N -io 2|3 2|3 9 3 A x+2 + B + x-1 C (x-1)² (x -…

A:

Q: Given √√2/10 dx, determine all value/values of P for which the improp хр onverges? A) {0,1} B)…

A: Topic:- application of integration

Q: The improper integral A e B C) O D 1 if the 0 ∞ ex dx is

A: Solve the integration  From 0 to ♾️ for the integrand e-x.

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

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: How many antiderivatives does a function of the form f(x) = x^ have when n0? (A) 1 B) none (C)…

A: