Find the total area between the curve y = 1- x2 and the x-axis over the interval [0, 2). Evaluate the integral using integration by parts i. ii. x2lnx dx 1

Q: Evaluate the integration by parts (5х)(сos(3x))dx 0.

A:

Q: 1 dx X+4

A:

Q: 16-y2 16 – 22-y drdy by using appropriate coordinate system. an

A:

Q: I) S dx/ (x² + 4x + 3) find integral

A:

Q: x² +1 dx (3x+1) 2. Evaluate

A:

Q: Evaluate the integrals

A: Consider the integration as I=∫01x2+xdx

Q: 8. Evaluate the integral 4 + 6x dx Vx

A: In this question we have to solve the integration given. we can write , x=(x)12

Q: QUESTION 9 (8 points) Use a change of variables to evaluate the following definite integral. S 6x dx…

A: The given integral is:∫12​(3x2+4)36x​ dx a.) Let u be the expression inside the parentheses in the…

Q: o f dx/ (x² + 4x + 5) find integral

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.