a) Determine whether the integral da 16 2x is improper or not. Justify your answer. b) Evaluate the integral 6 2x dz. (3x – 1)(4r + 5)

Q: 1.Simplify: -2xy[6x² + {-6x³y – 2x²y – 2[2xy – x(3x²y– 3x – 2y) - 3x²] + 2x(xy)}– 3x²] a.

A: Topic:- Algebra

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A:

Q: x² + 4x - 4

A:

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A: Given that: ∫(6x2-4x+1)dx

Q: 3/2n 7. Find proj in terms of: (a) b)

A: Solution of the problem as follows

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A: One property of integrals that will be used is ∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx. Another property of…

Q: Simplify. [(20)²]³ 8i Enter your answer in the box.

A:

Q: Vse Che quadatic farmuta to solve the quaidratic egaution?

A:

Q: óa b7 (a+b) (3ab) (3ab*)* Simplify the rational expression 3.

A: 6a4b7/(3ab)2×(a4b7)2/(3ab4)3 6a4b7/(9a2b2)×(a8b14)/(27a3b12)

Q: dx Evaluate f 4x- +4x+5

A: We have integral  I  = ∫dx4x2 + 4x + 5 Take 4 common from the denominator, we get I  = 14∫dxx2 + x +…

Q: 3.) Simplify (0.75x + 2y) - (0.3x – 0.6y)

A:

Q: Evaluate 3 (9x² – 2x + 1)dx 1

A: Given:∫13 9x2-2x+1 dxIntegrating formula:∫xn dx=xn+1+C

Q: Evaluate: / sec (5x + 1).5dx

A:

Q: Evaluate: Зх — 4 dx J 3x² – 8x + 5 ..2

A:

Q: Exl show that 9dx (x²+4)² 97 16 H.W

A: Here we have to show the above integral.

Q: Find determinent [3a 3b 3c -d -e -f 4g 4h 4i]

A:

Q: dx Evaluate 34 N2 + 3x - 2x

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Q: 1 da (2a + 1) +1) 1. 8.

A:

Q: Evaluate f (5x* - 8x3 + 9x2 – 2x + 7)dx

A:

Q: Evaluate: a) J 5x8+4x7+x6+7x²+3x-15 dx (x²-4)(5-6x)(x2+2x)

A: We use method of partial fraction to solve this integral. If degree in the numerator is more than…

Q: and simplify. (x-2y)(x + 2y) Select one: A. x² + 2y² B. x² + 4y² OC. x² - 4xy – 4y² D. x² - 4y²

A: Please see the answer below.

Q: When does a(b+c) result as a positive value for ac?

A: Note: If a>0 and b<0 then ab<0  If a>0 and b>0 then ab>0 If a<0 and b<0 then…

Q: Calculate √√3 8 2 1/√3 1 + x² dx

A: Given ∫13381+x2 dxTo evaluate the integral:

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.