Find the value of the improper integral or state that it is divergent. (If it is divergent, enter DIVERGENT.) co 1 dx 11 11 1 lim (t->) 1o 11A 10) - 11

Q: 3- I = xp- (x² + 1)²(x² + 2x + 2) Solve this integral by using Rezidue Therom. 8.

A:

Q: Show that cos A x e 2 *,x2 0. %3D

A:

Q: Use the Fundamental Theorem to calculate the definite integrals. 2 1 dx x+2 -1

A:

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: 20. Verify by differentiation that finx dx = x(In x-1) + C, then use appropriate changes of…

A:

Q: Late dx sec2 x (b) [*. dx /1 – tan² x VT(x+4) |

A:

Q: +z/3 + sin z dz

A:

Q: sin 2ydy 5.J7-3 cos 2y 15.

A:

Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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.