What is the integral of the shaded region? * 8(y)-f(y)dy A. OA OB Oc OD B. İf(y) - g(y)dy a C. f(x) - g(x)dx D. - † f(x) = g(x)dx| (x)dx|

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

A: Volume

Q: A solid is formed by rotating the area between the curves y = x and y = x² between x = 0 and x = 1…

A: To solve this problem we use washer method.

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: w/N Let f(x)=√√3x-2 on the interval y-axis and find the volume of the resulting solid. Revolve the…

A: Application of integration

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

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: A detailed solution is given below

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

A:

Q: s (x+1) log(x+1)

A:

Q: The gradient at any point (x, y) of a curve is given by dy-3x² +ax-36 where a is a constant. The…

A:

Q: Question 20 Determine the area bounded by the functions f(x) = (x + 1)³ and A unit² А 3 Ⓒunt² B 3 C…

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

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

A:

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

A:

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

A: To solve the given double integral.

Q: dx (x+1) log(x+1) 1 In[log(x+1)]+C In 10 -In 10 log² (x + 1) + C 2 In 10 In[log(x+1)] + C -aluate: A…

A: Topic:- application of integration

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 C=/2 A 18 cos²0d0 (B) 1852/200…

A: See the details solution in below

Q: 1 3√x + x X Solve the integral: J 6 5 F1+x8 + c A @ c in 1 B 1+x + C © n1+x.c C C Gin|5+x²|+C D - dx

A: Explained below

Q: Question 12 12/201 iven хр (A) {0,1} B (-∞,1] Ⓒ (-∞0,00) C (D) (1,∞0) -dx, determine all…

A: Topic:- application of integration

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: 17. Evaluate [9e³x dx O9e³c+1 3c+1 O9e3c O9ec-3 3e³c-3

A:

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

A: Now,The graph of the area bounded by f(x)=ex, g(x)=e-x and x=3 is shown below:

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

A:

Q: sinh xte cosh x + ndefinite Integral Sin(cosh x + e*)- In(cosh x + e*) sinh x te cosh x + ex

A: We have to calculate the given indefinite integral according to the given information

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

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

A:

Q: A B (C) D dx -2 (2x + 1)² (241) 2 2 (2x + 1)² ex - ln( 2x + 1) 8

A:

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: X √√x dx Solve the integral: (A) 3 B + C 6 с 6√√x +C D 3√√√x² +C

A: To integrate the following problem

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

A:

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 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: 1. ²₂(x² − 2xy² + y²³) dx dy

A: Solve the following integration .

Q: x+2 Determine the case of the following proper rational function after simplification: (x² – 4)(x³ –…

A:

Q: An engineer is designing the runway for an airport. Of the planes that will use the airport, the…

A: Given:   To determine: The minimum allowed length for the runway.

Q: Question 10 Let f(x)=√3x-2 on the interval volume of the resulting solid. 43x 135 83m 125 83x 135…

A:

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

A:

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming Ⓒ S A 1-z² B 1+z² © √ 1 +…

A:

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

A:

Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

A:

Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: 1 x + × olve the integral: 5 ® shi+x+c A C 5 6 ® $h1+x+c B C © 6n|5+x²|+c C D Shi+x+c C 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:

Q: Which of the following can be determined given f(x)dx=5, g(x)dx=7, and and T h(x) dx = -5

A:

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

A:

Q: Evaluating (A) (B S -3 of */2 si 57/2 18 18 ofth 0 (D) 9-x² dx using trigonometric substitution will…

A:

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: If f(x) = A B C D tanx S 0 1+tan²x 1+1² Ite' -dt, then f'(x) equals 1+ e tanx In (secx)√√1+tan²x…

A: