Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. HINT [See Example 1.] Between y = x and y = 1 for x in [-1, 1]

Q: Sketch the graph of y =-1/2sin (px). Which of the following matches your graph?

A: Given curve: y=-12sinpx

Q: X = --6t-1 2 Find all points on the graph of that have either a vertical or horizontal y=- -9t +1 3…

A: Here given x=3t22-6t-1y=t33-9t+1

Q: 42. The figure shows graphs of f. f'.", and f". Identify each curvc, and cxplain your choices. abed

A: In the question we have to decide graphs.

Q: The curve y et and the lines y = 0, x = 0, and x = In 2 %3D

A:

Q: You need to interpolate the Y data at X= -17 and X=13 using the data table below. X -25 -3 7 25…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: -4 マナ -4 4 4 -4 -4

A:

Q: g(x) is concave down at (-7,-3), concave up at (7, 10), and has an inflection point at (2, 4).

A: Given :- function is concave down at (-7,-3) concave up at(7,10) and inflection point is (2,4)…

Q: k-x k²+x² Sketch the graph of K= const-

A: k is constant  so drawing it for  k=-3,-2,-1,1,2,3

Q: A trough 4 feet long and 1 foot high is filled with water. The vertical cross-sections of the trough…

A: Given that    A trough 4 feet long and 1 foot high is filled with water. The vertical cross-sections…

Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: Find the exact length of the curve. 1 x² -In(x), 1< x < 8 4

A:

Q: Meeting Write the equation(s) of the tangent line when x = 0 2 x² + y² - 6x + 6xy = 16

A:

Q: WAM Which of the following graphs is the correct plot of y = – 2 cos(x)? -1 -2 -2 -2 -3 -4 -4 -1 -3…

A: We have to draw

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.