Use the method of partial fractions to evaluate each of the following integral. dx Jalx – 1)(x – 2)(x – 3) 1) In|1– x| -in|2 – x| +ln[3 – x] -in|x + 2) 을m1-지-3미2-지 -jm3-지-jm지 +C 3) 를미1-지-3 m2 -지 +승m3-지 +능m지 + C 4) 111-지+1m2-지 +승m3-지-jim지 +c

Q: 1. Evaluate the following definite integrals: 2 b) 3x3 (3x4 - 2)5 dx re-(z2−1)/2 dx

A:

Q: Determine the following integrals. f(x² −5x+6)dx a. b. 4 √(²²-27) dr dt C. √√√x³ dx d. f(x^2 + 2x +…

A:

Q: Make a substitution to express the integrand as a rational function 3 f dx x²+x√√x

A:

Q: The graph below shows a function f(x). Determine whether each of the following integrals would be…

A: We want to know the area of the given graph is positive or negative on the given intervals.

Q: Evaluate the integral √(4 by making the appropriate substitution: u √ (432² dx [ X (4x² + 11) 7 = X…

A:

Q: 8a + 20x dr. x* + 5x² + 6 Evaluate the definite integral

A: We can evaluate the integral as below.

Q: Write the integral as the sum of the integral of an odd function and the integral of an even…

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.