22 Calculate the value of the integral over the following C curves, a) C:|2+1| = 1

Q: suppose A is a positive real number, determine the area of the traingle enclosed by the lines x=0,…

A:

Q: 53. Use the substitution u = x + 1 to evaluate the integral I dr.

A: Differentiate u with respect to x,  du= 4x3 dx du/4x3= dx

Q: In x dx a/1+(ln æ)? (In x 2

A: We have to evaluate the given integration

Q: c) Find the value of (Log:)² where the integral is along a contour not intersecting the branch cut…

A: We find value of given contour.

Q: Use six rectangles and right endpoints to estimate the area under the curve f(z) = V2x on [0,3).

A:

Q: 3) a) Use Simpson's rule with n=4. b) Estimate the error in the approximation. -2x dx jedx to…

A: Given integral is ∫06e−2xdx. a We have to approximate the given integral by using Simpson rule.…

Q: Evaluate the integrals in ∫log10 x/x dx

A: Given integral is: ∫log(10x)xdx To evaluate this integral, first apply the logarithmic property…

Q: Evaluate the following integrals: - TVī + vi csc(t) (a) dt

A: The given integral,∫t2-πt+t csc(t)tdt

Q: O Use the MVT for integrals to show that there is point c in the interval (0,4) such that sec² (c) =…

A: MVT Theorem: Let f(x) is continuous on [a,b] and f is differentiable on (a,b). Moreover f(a)= f(b)…

Q: Q1) Evaluate the following integral: y : tanx dx

A: To solve this question, We will use the identity- 1+tan2x = sec2x

Q: Find the area between the curve of y ਆਗੂਆਂ 2 4 = zæ + 2 and the x-axis on the interval [-2, 1].

A: Given that , Now we want to find the area between the curve and the axis  on the interval .

Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

A:

Q: de Use contour integration to evaluate the real definite integral 17- 8сos(®

A:

Q: V 11y2 – 15 dy y2

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.