15 Evaluate the improper integral J. (x- dx

Q: 10. Evaluate the integral. dx x²/4 – x²

A:

Q: •1 3 25. dx Jo x5

A:

Q: dx

A: Given  The improper integral is ∫011xdx.   Formula :- Power rule of integration :- ∫xndx=xn+1n+1+c

Q: x + 1 dx i x² + 2x 0, 15. 8.

A: We have to solve

Q: 11. Evaluate the integral. +3 x² + 4

A:

Q: S (1 + In x)² x -dx

A:

Q: xe (b) Evaluate the integral dx. (1–x)*

A:

Q: Evaluate the integral.

A: Given: The integration∫10(x-1)(x2+9)dx To evaluate: The given integral.

Q: dx Evaluate the improper integral J x(Inln x )

A: We have to find value of given definite integral

Q: Evaluate the improper integral. xp 1 x(5x + 3) 8.

A:

Q: Evaluate the integral 169 dx S 13 x(Inx) 4

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.