(x1x >3] = S ded(x-3) dメ 3

Q: A. Using the basic formulas, integrate the following: 1. S(x* – 2x3 + 3x? – 1)dx 2. S(2x – 5)?dx 3.…

A: Explanation of the answer is as follows

Q: Find the integral of: Зx2 — 4 - x2

A: From the given problem:   I=∫3x2-4x2dx ....(1) Now simplifying: 3x2-4x2=3-4x2 Now substitute this…

Q: 1 ut du. 8 13

A:

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

A:

Q: 24.) The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find the rate of…

A: Area of the circle , A =πr2 ; where, 'r' is the radius.

Q: - a²(x²-y?) dx dy Exercise: Finish ter 8.

A:

Q: The integral dx Vx² – 4 3 -2

A: To evaluate the given integral

Q: Rewrite the integration in terms of u. 2x dx = du x² + 16

A: Given :∫032xx2+16dx

Q: 6x+13 1. Sx²+5x+6 - dx Co² (²) du

A: Dear Learner,We expert are following bartleby expert guidelines to answer the Questions. In case of…

Q: Determine the following integral: 3x + 3 Jx2 + 7x + 12 as a function of x.

A: First we will factor the denominator of the integrant and then by doing the partial fraction we will…

Q: 5x + 6x iii) dr p³ – 3x2

A: Given: ∫x4-5x3+6x2-18x3-3x2dx

Q: Evaluate the integrat. Sa dx су-хууг dx

A: Given :∫14-x22dx

Q: 1 dx Vx - 1|

A:

Q: ral L9/x? + y') dxdy.

A: Solution :-

Q: · (x²-3)dx refer to ſ x-2 The given indefinite integral can be solved by Algebraic Manipulation,…

A: Given∫x2-3x-2dxTo findquotient and remainder while we do long division.

Q: Sx (3-2x dx

A: Given that a function and we find the integration of this function by using reverse chain rule.

Q: Perform the following integrations: 9. 10. dx

A: To evaluate the given integral.

Q: Evaluate he followring integral 4

A:

Q: -1 3 ترجم V 4 x² 4 + 4 dx

A:

Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

A:

Q: 12. Compute [ ft 2y Suggestion: Change the order of integration e-y/x dxdy.

A:

Q: xy? Find R -dA, R = [0, 2] × [- 1, 1] x2 + 1

A:

Q: Evaluate xe-2a dx {Hint: Integration by parts} Oe-2r (플 + 1) + C O-e-20 (플-1) +C O-e-a (블 + 4)+ C…

A:

Q: what is the difference between LIf(x)[ dx and Lif(x) dx

A:

Q: v(v² –1)dv v2 +1 3.

A:

Q: (2x2-3x+2) dx (x-1)2 (x-2) - Evaluate the following integral: S

A: To evaluate the integral: ∫(2x2-3x+2)(x-1)2(x-2)dx

Q: 3.53 dx Compute 3+9,2

A: I=∫013313+9x2dx=19∫01331x2+13dx=19∫01331x2+132dx Since, ∫1x2+a2dx=tan-1xa

Q: Integrate the following: dx 1. a) V9x² +12x-5

A: Solution:-

Q: Evaluate the following integrals: x +1 1- dx (x² + 2x + 2)3

A:

Q: 1 .2 2 dx = 0 xe 0- -

A: Given: 12π∫-∞∞xe-x22dx=0   We know that; ∫eax+bdx=eax+ba+C     Note: As per Bartleby guidelines we…

Q: c) S ¥2x2 1+2x2 -dx-

A: Let consider the denominator term = t

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.