X5.5.21 Evaluate the integral. dx Vx (7 +9x) dx = Va (7 +9/x)*

Q: A driver has to pay an annual road tax of $150. His car does 50 kilometers to one gallon which costs…

A: For the solution of the problem follow the next steps.

Q: y"+9y=7e^x find general solution

A: Given- y"+9y=7ex To Find- The general solution of the above differential equation.

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.