State the trigonometric substitution you would use to find the indefinite integral. Do not integrate. x²(x² – 49)3/2 dx

Q: Integrate .5 X 12 1+x

A: Integration by substitutions

Q: Find ∫sec2 (5x + 1). 5 dx.

A: we have to find the value of the given indefinite integral. ∫sec25x+1·5dx

Q: dx 1+ 3/2 х

A: We need to integrate the given integral.

Q: x V2x – 1 dx dr

A:

Q: Complete the table to find the indefinite integral. (Use C for the constant of integration.)…

A: Note: We know that integration of x^n is given as x^(n+1)/(n+1) + C. Where n not equal to -1 and C…

Q: Evaluate Set 7x cos (6x) dx. Sex cos (6x) dx =

A:

Q: dx 19. S 2-x

A: Given: ∫dx2-x

Q: dx 28. 1– x4

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.