A rectangular swimming pool is 46 ft wide by 75 ft long. The table gives depths (d) from x = 0 at the shallow end to the diving end. Use the Trapezoidal Rule with n= 15 75 to estimate the volume of the pool, V =| 46 • d(x) dx. 15 20 d 46.2 | 7.2 | 7.9 | 8.5 55 60 65 70 75 12.4 12.7 5 10 25 | 30 35 40 45 5O 9.5 | 9.9 |10 10.7 11.1 11.4 11.7 12.

Q: 5. Evaluate: (а) ( 5х* -х-4) dx (b) f( 2x +4)(3x + 6)dx

A: 5. (a) We will evaluate the integral ∫5x2-x-4dx

Q: 2. Find the area of the shaded region. -1.0 -0.5 y 8 6 y=3e* 4 2 0.5 (1, 3e) y=3xet² 1.0 1.5 2.0 X

A: The bounded region is given in the graph, we have to find its area.

Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

A:

Q: A trapezoid JKLM is dilated through the origin by a scale factor of x. How does the area of the…

A: Suppose a trapezoid JKLM with coordinates, Jx1,y1, Kx2,y1, Lx4,y2, Mx3,y2 be dilated by a scale…

Q: The graph of the derivative f'(x) of f(x) is shown. Compute the total change of f(x) over the given…

A: Graph of f'(x) vs x is given. Here, f'(x)=∆f∆x Therefore, change in f(x) will be, ∆f=f'(x)·∆x It…

Q: 3. 3.5 m 21 m

A: Simple area problem.....

Q: The shape of a dragonfly wing can be roughly modeled by the shape between the curves y = √x and…

A: see the graph of the functions

Q: . Find the value of z based on the given area for each figure below. (a) A = 153 square feet (b) A =…

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.