Use the Fundamental Theorem of Calculus to evaluate the following definite integral. S² dt

Q: Find an antiderivative F(x) with F'(x) = f(x) = 6e² and F(0) = 4.

A: F′(x)=f(x)=6e2x and F(0)=4

Q: Evaluate: [8zº · sec² (25) dx =

A:

Q: Stoite the Fundamental Theorem of Calculus?

A: we need to write down the fundamental theorem of calculus.

Q: Given that ß = 101°, y = 24°, c = 15. Which of the following equations solves for a? a) a = (15 sin…

A: Given that the triangle we have to find choose the correct option

Q: Find the vertex, focus, and directrix of the parabola with the given equation. Graph the equation.…

A: The given equation of parabola is The vertex form of parabola with the vertex  is

Q: Let xy = 4 and dx dt Find dy dt when x = = 2. 1.

A: ..........(i)Differentiating equation with respect to t Put   ..........(ii)

Q: amount for 6 Three kinds of tickets are available for a concert: up-front, main- floor, and balcony.…

A:

Q: Find the mass of the solid bounded by the planes x + z = 1, x-z=-1, y = 0, and the surface y = √2.…

A: Given that the solid bounded by the planes  and the surface .The density of the solid is

Q: Find the radius of convergence and the interval of convergence of the power series. n=0 nx 3…

A: The solution is following in explanation step.

Q: A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and…

A:

Q: dy Write the function in the form y=f(u) and u = g(x). Then find dx y = 9 8x 5 U= (Type an…

A:

Q: If g(s) = * · 86 0 g'(s) = √5 + x7 dx, compute g'(s).

A:

Q: Given f'(x) = 6x + 5, compute f(4) – f(1). -

A: Explaination of the answer is as follows

Q: 8. Evaluate the definite integral. a. 6 e² + 18 e² + 18z dz

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 0 1 2x (4 – x²) dx

A:

Q: TU Find the speed for c(t) = (3 sin(5t), 8 cos(5t)) at time t = FR

A:

Q: A particle travels according to the velocity function shown below. Find the displacement of the…

A: The objective of this question is to find the displacement of a particle that moves according to a…

Q: tinues to grow for a while, but then stops growing and begins to decline. The +124t-12312. Find the…

A:

Q: r = sin(20), r = cos(20)

A: Given that the polar curve

Q: Let A(x) = √² ƒ 4 3 T -2 el -4 -5 * f(t) dt, with f(z) shown in the graph below. 3 At what a…

A:

Q: X 5.8 6.0 -0.9 6.2 f1 (x) Selected values of the derivative of the function f are given in the table…

A: The given tablex5.86.06.26.4f'(x)-0.93.21.9-1.3

Q: Consider the problem min x2 + 2x2 such that r₁ + 2x₂ = 3 #1.22 The bordered Hessian for this problem…

A: The problem is given as,such that

Q: Differentiate the functions: cosec x * cos x

A:

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WO FOR BETTER…

A:

Q: Given f is concave down and ƒ (4) = −2 and f1 (4) = 3. What is the estimate for = 4? Is it an…

A:

Q: Evaluate the following integral. 2 | (0²-0 -2 (4y -6y+6) dy

A:

Q: What is the domain of the function shown in the graph below? -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10 9 8 7…

A: To find the domain of the function shown in the graph below.

Q: Air freshener A has a mass of 42 grams when opened and its mass decreases by 4.2 grams each day. Air…

A: The mass of the Freshener a=42 gmIf opened in the air decreases to  4.2% per dayThis means the decay…

Q: At time t=0, a particle is located at the point (1,5,4). It travels in a straight line to the point…

A:

Q: 1 if x > 0 - 1 if x < 0 c. Find the domain and range of f. Let f(x) = .a. Find f(-16) and f(14). b.…

A:

Q: Suppose that functions f and g and their derivatives with respect to x have the values shown to the…

A: As per the company's guidelines, we are supposed to solve the first three sub-parts for you, Kindly…

Q: Suppose value of [ f(x)dx 2 f(x)dx. f(x) dx = -1, [**f(x)dx = 4 and [ f(x)dx = 2. Find the

A:

Q: Find the derivative of  f(x)=X4.23x

A:

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A: The objective of this question is to understand the graphing strategy for the function f(x)= 5x^3 -…

Q: Click on the graph to view a larger graph Use the Law of Sines to find the indicated side a given in…

A: Given,

Q: If c = 180, ZA = 82° and ZB = 47°, b =

A:

Q: Determine the integral using the substitution u = √√x+11. √(x +11) 1/2 √x+11 dx

A:

Q: Write the integral required to find the area of the region pictured below that is bounde 2(y+2) 3…

A:

Q: Find all points where the function is discontinuous. TO 16 NO NO 6 18 Ay

A: The graph of the function isTo determine: The points where the function is discontinuous.

Q: A curve with polar equation r = 28 5 sin +41 cos 0 represents a line. This line has a Cartesian…

A: A curve with polar equation represents a line.To find the Cartesian equation of the line in the…

Q: Sketch the graph of the function shown below. From the graph, find its domain and range. |xif -3<x<0…

A:

Q: Use trigonometric identities to solve the equation in the interval [0, 2). 2 cos ²0-sin 0-1=0

A:

Q: Hello, can someone please help me with this calculus practice question

A:

Q: is it 3and -2 for A?

A: A critical point of a function f(x) is a coordinate where the derivative f'(x) =0 for the x…

Q: 9. In the following exercise: i. Identify the function's local extreme values in the given domain,…

A: As per the company's guidelines, we are supposed to solve the first three sub-parts for you, Kindly…

Q: Given 6xy= 2 + y³ ,  a) Find the coordinates of a point on the curve at which the line tangent to…

A:

Q: Note that: An interior point of the domain of a function f where f' is zero or undefined is a…

A:

Q: If the velocity of a car is given by v(t) = 90 for all time t ≥ 0, then the position of the car for…

A: The velocity of a car is  for all .The aim is to find the position of the car.

Q: Find the indefinite integral. [9√ w dw = +C

A: We know that,.We have to find the integration of .

Q: Write the given expression in an expanded form. Assume that variables represent positive numbers.…

A: Let