Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume x >0 and y >0.a. ln xy = ln x + ln y.b. ln 0 = 1.c. ln (x + y) = ln x + ln y.d. 2x = e2 ln x.e. The area under the curve y = 1/x and the x-axis on the interval[1, e] is 1.

Q: QL. Find the area under the curve for following equation for the interval (x= 0 to x = 8) 1 y = (x-…

A:

Q: Consider the value of t such that 0.01 of the area under the curve is to the left of t Step 2 of 2:…

A:

Q: valuate the following integral 2d.x (3(ln x)2 + 12 In x – 15)

A:

Q: 5 Find the area under the curve y over the interval [0, 1]. (4x + 4)2 Enter the exact answer. area =

A:

Q: Calculate the integral approximation S10 for Si, dx. 1 x5+1 S10 =

A: Let's find integration value by using simpson rule.

Q: Verify that the area under the curve y = 1/x from x = 1 to x = m equals 2m, the area from x = 3 to x…

A:

Q: If you want to approximate the area under a positive curve y=f(x), from x=-5 to x=6, using 7…

A: The given question can be solved as shown in step2.

Q: Evaluate the integral: |x cosh x² dx sinh x +C 2 x sinh x? +C sinh x? +C x² sinh 2x +C

A:

Q: Determine the area between the graphs of the equations y=x and y=(x)^2-1. Integrate over the x-axis…

A:

Q: Sdr +a

A:

Q: Find an expression for the area between the curves y = x-/2 and y = e between the lines X = 0 and x…

A: In this question we have to find the expression for the area between the curves.

Q: 4. a. Use the Fundamental Theorem of Calculus to find the exact value of 3 (x3 – 4x)dx. | b. Find…

A: Solving the definite integral we have

Q: Find the area under the graph of the function over the interval given. 13) y =ex; [-9,4] A) e 13 B)…

A: Given function is., y=ex [-9, 4] find the area under the curve. We know that, ∫exdx = ex + C

Q: Evaluate the following integral using integration by parts. Saxe 5x 3x e dx Evaluate the integral.…

A:

Q: Determine the Equation from the information below: HA: none X-Int: (0, 0) VA: none Y-Int: (0, 0)…

A: The graph of a straight line crosses the x axis at the x-intercept and the y axis at the…

Q: Find the area between the following curves. x= -3, x= 1, y=e^, and y-3- e 2 (Type an exact answer in…

A:

Q: Q1. Find the area under the curve for following equation for the interval (x = 0 to x = 8) 1 y (x –…

A: Area under the curve will be given by integrating the function of the curve with respect to x with…

Q: Determine the value of z such that the area between 0 and z is 0.2673 and z is positive. Round the…

A: Normal distribution is a continuous distribution which has many real life applications. Normal curve…

Q: y = e from x=0 to x=1

A:

Q: b. Find the area bounded by the curve y = Vxe-Vx and the x-axis from x = 0 to x = 4. (45 Ivarks)

A:

Q: Find a formula for the area A(w) of the triangle bounded by the tangent line to the graph of y = In…

A:

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact…

A:

Q: 1. Find the area between the curves of y = x2 +1 and y = x +7 from x = -2 to x = 3. Round to two…

A: Topic-application of integration

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact…

A: The given integral,      ∫33316x-33dx

Q: 1. Find the area under the curve y a. f(x) = x³ [2,3] b. f(x) = 3√x [1,4] (x) over the stated…

A: a) fx=x3          2,3 b) fx=3x          1,4 Find the area under the curve y=fx over the stated…

Q: Can i get step by step help with problem

A: To write the relationship

Q: The functions y = x² and y 0 < k < 1. Without finding the value of k, setup an expression which…

A:

Q: Find the area bound by y = 1, y = ln(x), x = 0 , and y = 0.

A: Let's find.

Q: Show that if k is a positive constant, then the area between the x-axis and one arch of the curve y…

A: y = sin kx cuts the x axis at y=0. Solve for x.

Q: h. fx2 Vx3 + 2dx

A: Integrate by substitution

Q: Find Ln, Rn and their average value for the definite integral using the indicated value of n. dx, n…

A:

Q: Use the definition of the definite integral to solve the given problem. a. Find the area of the…

A: Given: The curve yx2+12=x3⇒y=x3x2+12, y=0,x=0,x=1 To find: Area of region bounded by these curves.

Q: c. Set up the definite integral that gives the area of the region inside the circle but outside the…

A: c) The equation of the circle is, The equation of the loop is

Q: Consider the value of t such that 0.01 of the area under the curve is to the right of t. Assuming…

A: Given Information Significance level =0.01 Degrees of freedom = 28 t-value = 2.467140098( Using…

Q: 4. Find the area between y=Z+3. and ys-xt1ox-9

A:

Q: e. Find the area under the curve y = vx + 8 from x = -8 to x = 4. Give exact answer.

A:

Q: I. Evaluate the following integrals. 1. J 1 - coth² (log₂x) dx x cosh (log₂ x)

A:

Q: In each integration problem sketch for yourself a corresponding graph to ensure that your answer is…

A:

Q: Find the area between the curve y = 1/x7° and the x-axis from x = 1 to co. square units

A: Given: The area between the curve y=1x76 from x=1 to ∞ To find the area of the curve. The formula…

Q: 4) The area between y = In x and y = 2ln x up to x= e is:- = 7 A) B) = 1

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: 1 dV E O Volume of solid E O Mass of solid E O none of these above O Area of solid E

A:

Q: 12 Find the area under the curve y = over the interval [ – 1, 1]. (x + 2)² area = i

A:

Q: Set up a definite integral that represents the shaded area. O A. f(x) dx Ny 18 | f(x) dx В. 4 C.…

A: Option (d) is correct.   in this graph, function f(x) belong between 0 and 3 then lower limit is 0…

Q: Find a formula for the area A(w) of the triangle bounded by the tangent line to the graph of y = ln…

A: Given  y=ln x11y=11(lnx) We need to find out the tangent line. First we find out the slope To find…

Q: 4. Find the area under the following curves over the indicated interval: (c) z = -3t2, y = 2t, for 2…

A:

Q: y = sinx from x=0 to x=n

A:

Q: Findl the specitie intearals (show calkoladion e 1) x' (In+) dx 1.

A: (1) Consider the given integral: ∫1ex2lnx2dx Apply the rule of integration by parts:…

Q: 10. Find the area between the graph of y = and the x-axis for x E [0, b|] where b is a (2x² + 1)²…

A: Please refer the attached image for complete solution. THANK YOU.

Q: (8) Find the area under the curve f(x) = e* – 1 from X =1 to x 2 Leave the answer with e, don't use…

A: SOLUTION-

Q: 1. Approximate the area under the curve of y = e¯** from x = 0 to x = 1 using: a. R4 h Le %3D

A: Reimann sum

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.