Find the area of the region between the graph of y=x+2, above x-axis, and between the lines x= -1 and x= 1

Q: Graph the curves  y= x2- x  and  y =  x3 - 4x2 +3x  on acommon screen and observe that the region…

A: The given curves are as: y=x2-x   & y=x3-4x2+3x First of all we have to find the point of…

Q: Find the area of the region bounded by f(x)=-x^2+6x-5, the x axis, and the lines x=2 and x=5. Graph…

A:

Q: Calculate the area of the region that lies between the line y=-1 and the parabola y = x²-6x-1,

A:

Q: the shaded area shown in the figure is bounded by the line with equation y = 12-7x-x² and the line…

A: given functions are                                              y=12-7x-x2, y=4…

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.