Q.2. Calculate the integral of: f(x) = (3x+1) from a=-0.2 to b=0.6 by using Simpson's Rules only and taking 5 segments for the solution. J&| should be smaller than 0.3%. %3D

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

A:

Q: please. 1. Find the area in the first quadrant bounded by f (x) = 4x – x² and the x-axis. 2. Find…

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Q: 2dx J x (3(ln x)2 + 12 In x – 15)

A: The given integral can be evaluated using the factorization and substitution technique.

Q: Dat

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Q: find the length of the remaining part of the y = x³/12 + 1/x curve between the x = l and x = 2 apfog…

A: We have to find the length of the remaining part of the curve y=x312+1x between x=1 and x=2

Q: Find the exact area between the graphs of f (x) = 2x +1 and g (x) = 9 – x2. First find out where the…

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Q: A. Evaluate the following integrals by substitution. 1. fx(2x2 + 3)%dx x5 2. S; dx (x6-8)2 3. Sx V1-…

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Q: 1) Express , 4xyz dV , where E = [0,1] x [0,2] x [0,3] by using different orders of integration.…

A: In the given question we have to find the integration ∫∫∫E4xyzdVwhere E=[0,1]×[0,2]×[0,3]  is the…

Q: x5 dx (x6-8)2 2.

A: given that,  evaluate the following integral ∫x5(x6-8)2dx integration formula   ∫xndx=xn+1n+1+C

Q: Let f(x) = 3 x² +6. x +4 and g(x) = 4 x² + 8. x +3. Write down an expression to calculate the area…

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Q: 00 for For two independent lives age 40, you are given that H40(t) t< 60. Calculate Var(T40:40). %3D

A: It is given that two independent lives age =40. Also given, μ40(t)=80-t for t&lt;60. μ40(t)=80-tt…

Q: (x, y) = ( = ) (smaller value ) (Larger value)

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.