Find the indefinite integral J J9+x? dx using an appropriate trigonometric substitution.

Q: An elementary reaction is generally expressed as: dC, = -kC," %3D dt

A: Given, dCAdt=-kCAn now solve this integral dCA=-kCAndtCA-ndCA=-kdtCA-n+1-n+1=-kt+c at t=0…

Q: Consider the integral x2 dæ, (x² + a²)³/2 where a is a positive real number.

A:

Q: /9-x² dx. Use trigonometric substitution. x2

A: This question is related to indefinite integration, we will we will solve it using given…

Q: dx x' +9 2. Use an appropriate trigonometric substitution to rewrite as J(a simplified trig function…

A: Solution: The objective is to find the value of given integral

Q: V 6² — (x − a)². b) Use a trigonometric substitution to evaluate the indefinite integral. s dx You…

A:

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.