Evaluate the following iterated integral. -7cose 5 rdr de 49 2n+5sin 40 49 n+ 5sin 2n+ 5sin 40 () 49 In+ 5sin 40 49 2n+ 5sin 40

Q: Find the integral. [5(1²-5t-2) dt O 5t³-5t² - 2t + C O 5/3 +³ O t³ - 5t² - 2t + C 3t³-t²-2t+C O 10t…

A:

Q: 12) -5Vx 2 + + 6Vx) dx 3 11х A) + C 3 2 1 1 3 3 В) -Зх° + 2х° + 5х° + C 4 6 3 5 С) -3х° + 2х* + 5х°…

A:

Q: evaluate the integral. | (3si + 6s²j+9k) ds

A: Compute the integral of each component separately. Then combine them to get the result.

Q: U V3-22- zt

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Q: 7 N 3 + -4√2 + √z dz

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Q: et dt (e2t +8et+7)z

A: Here we have to evaluate I=∫ete2t+8et+732dt

Q: in how many different ways can 7 potted plants be arrangesd in row

A: We can arrange n things in n! ways in a row.

Q: Evaluate the following iterated integral. -7cose 5 rdrde 49 n+ 5sin 40 49 2n+ 5sin 7 2 n+ 5sin 40 49…

A:

Q: Which of the following integrals has an integrand that is a proper fraction? 2x5 -x + 4x3 -3x2-5x+4…

A: Proper fraction is the sum of partial fractions, The give integral have factors in the denominator…

Q: Evaluate -2セ 34 L{+(e 2te

A:

Q: 2z I 2 L (2,1, 2) dydadz I = -2/2 8 _z2 D I= f(x,y, z) dydxdz +2 2z-12 8 z2 22 2 • 2/2 8 z2 I = f(x,…

A: Given the triple integral

Q: -2 2 7e" + dy -5

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Q: 1² +3 dr. Compute the integral 1² – 3r + 2

A: Derivative of a function f(x) with respect to x is the measure of how fast the function is changing…

Q: Evaluate the integral.

A: Given:            ∫461t2-9dt

Q: Sy+ –3-dy у (3–2) 3

A: Our Aim is to find the integral of ∫y+3(3-2)23dy -(i)

Q: 1: Without evaluating the integral, show that z+1 U₁₁-2² 24-42² +31 VI 4개

A: From the given problem we get,

Q: Evaluate the integral (1 + 2y)ªdy.

A:

Q: 1 } [4ti 0 4ti +6t²j - 12 7K] (1+t) 4 k dtl

A:

Q: 3. Inx si sv² flax ye ² dz dx dy Y 0 S

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.