Determine the area bounded by the curves x³ - y = 0 and y + 3x² − 4 = 0, using a vertical element. Which of the following area in integral form is correct? (A) none of the choices B A = (x³ + 3x²-4) dx ⒸA=- A = - (x3 + 3x²-4) dx (D) 4-0 -S₁ -x²³+4x) dx x4 Ⓒ A = √ (-3³ - ++ +48) de. S² E -8 4 -2 S -8

Q: B $S₁ (x+2)(x-1)² = √[=42+²1+ (-₁2). (x 1)² ]dx, 1 x-1 A B C If -io 9 -ja -ia 2/3 1 2|3 2/3 2 the…

A:

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: Evaluate the double integral: 5 A 3 B C) D m|w 8 +10 √² √V ₂. Sª S 2ydydx 1 2

A: To evaluate: ∫14∫1x2y dy dx

Q: y = tan e³x + etan3x

A: (tan x)' = sec2(x) (eax)' = a eax.

Q: 3x e 1+e³x 13. What is the best substitution to make to evaluate S O u = 3x Ou = e³x Ou=1+e³x O u =…

A: A detailed solution is given below.

Q: ㅇㅇㅇ 고 |= 15 n y7

A:

Q: area of a rectangle is fixed at 60 square meters. The base is increasing at a constant rate of 2…

A: Given the query is to rate of change of height.

Q: en [_²_f(x) dx = 0 and ² fl Given f(x) dx = 11 6 T evaluate √3f(x)dx- -S__2f(x)dx.

A:

Q: πT Evaluate the integral: S sin(3x)cos(3x) dx

A: We can solve this as follows:

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx

A:

Q: Solve

A: We have to calculate the given indefinite integral

Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

A:

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

A: answer is in next step

Q: Find the rate of change of total profit, in dollars, with respect to time where R(x) = 7x and dx…

A:

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

A:

Q: |x-4|dx

A:

Q: The integral of x^7(2x^6 - x^8) dx with limits -5 to 5

A: Evaluating the definite integral

Q: Let f(x)=√√3x-2 on the interval volume of the resulting solid. 43x 135 83x 125 83x 135 43x 125 B 0 D…

A:

Q: Evaluate the improper integral 3 A 4 B O diverges N|9 름 12²233/30 dx

A:

Q: If g(x) = - [e' - In(2t+1)]dt, find g''(x) . dx A e* -In(2x+1) 4 B (2x + 1)² 4 C (2x + 1)² 2 D (2x +…

A: To solve the following problem

Q: 25 5+7x x dx

A:

Q: L₁ |x|dx

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: dy 53.x = dx Vx2 -4, x = 2,y(2) = 0

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: If fx and gx are integrable on the closed interval a, b, and k is a constant, then to determine wich…

Q: Question 5 3 Evaluating √9-x² dx using trigonometric substitution will lead to: A 35*1/2 cos²0d0…

A:

Q: X-2 dx Evaluate the integral: Sein(x²+3x-7) A x²+5x+In|3x-6|+C B ++ In|3x-6|+C 2 5 © +²2+5x+In/x-21…

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

A:

Q: Sx² + 4 ; x<2 Question (4): Using the definition, determine whether the function f(x) = (3x + 2 = ;…

A: here we have to check from left hand side of x = 2  and right hand side of x = 2 it means lim…

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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: 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: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A:

Q: Evaluate the iterated integral. r4y *x + y [IT*** 6xy dz dx dy

A:

Q: 3 √√²h(x) dx = -5 3 3 which of the following can be determined given f(x) dx = 5, g(x) dx = 7, and 3…

A:

Q: Find the slope, if it exists. x = -6 Select the correct choice below and fill in any answer boxes…

A: Given x=-6 The graph is

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

A: Conic method

Q: x+2 Determine the case of the following proper rational function after simplification: (x²-4)(x³-8)…

A: The first problem is related to simplification and second one is related to linear composition.

Q: z/3 1 + (cos 0 )2 (cos Ꮎ ) 2 ᎾᏢ .

A: We have to find the solution

Q: R is the region bounded by the functions f(x) = 1 - 3 cos (x) and g(x) = 4 sin (x). Find the area of…

A: Ans : A=12 unit2

Q: 8. 3. √1 - 9t² dt

A:

Q: Question 17 The improper integral A 00 B) e C) 0 (D) 1 if the 0 edx is

A:

Q: Please show work! The area of a rectangle is fixed at 60 square meters. The base is increasing at a…

A:

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: 15. Iv X V9 – x2 - dx

A: We want to integrate the given function.

Q: L²x√x-2dx

A:

Q: dx √81+16x² S

A:

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

A:

Q: Draw a graph to match the description given. f(x) is increasing over (-∞o,-5) and decreasing over…

A: