(c) e="(cos(y)dr + sin(y)dy) where C is the square with vertices (1, 1), (1, –1), (-1, –1) and (-1, 1). (d) / F• dĩ where C is the ellipse ř(t) = (3 cos(t), 4 cos(t), 5 sin(t)) for o

Q: dx 1+4x2

A: We have to find out the integral of given function

Q: Evaluate the following integrals.

A: We have∫x21−9x2dx

Q: Evaluate the following integrals, clearly showing all of your work.

A: Step 1: Step 2:

Q: 4. Let 0 ‡ b, c E Rn and define A = be E Rnxn. Show that (a) R(A) = span{b}, (b) N(A) = {x ≤ R" |…

A: (a) We are given that A = bcT                    where, c ∈ Rn     So, R(A) = { Ax : x ∈ Rn×1 }…

Q: valuate the following integrals

A: Note: Since, we are authorized to answer three subparts at a time, therefore we are answering the…

Q: complete

A: We will solve the integration.

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.