Consider the following integral (Py+v)dA where D is the shaded region given in the figure below YA

Q: Evaluate the integral | y? dA by making an appropriate change of variables where D D is the…

A: According to the given information, it is required to evaluate the integral by making appropriate…

Q: Evaluate the integral by any mothod d choice: dx (b) e* dx

A: Consider the given: ∫1x-x3dxApply u…

Q: se integral to find the area of B.

A:

Q: x dy - y dx

A:

Q: S 2x. e*dx а. 4 3 b. J 20(2x + 1) dx

A: Part(a): Let the given integration is, I=∫2x.exdx

Q: Lm e7x dx 00

A: This question is based on definite integral.

Q: Compute the integral: -3 dz (z – 2)*

A:

Q: Use U-substitution to find the integral: 2 1 dx

A: Given,          ∫1x22-1xdx

Q: Evaluate |- 1 =dx. a) xVx* +1

A: Given: ∫1xx4+1dx

Q: Refer to the figure to the right. Set up a definite integral from a to b that represents the shaded…

A: The figure given in the problem represents the graph of y=f(x). the shaded area under the curve is…

Q: Convert the double integral (∫0 to 2π ∫1 to 2 (cos θ − sin θ)r dr dθ) to rectangular coordinates

A:

Q: E 3y dx dy Evaluate the integral

A: Consider the given integral  ∫01∫-1-y21-y2 3y dxdy

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.