use the Lagrangian method to solve: U=x1^(1/2)x2^(1/2) subject to 50=5x1+10x2

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A: First evaluate the integral by substitute method. Then apply the limits of integral.

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A: clc;clear all;close allx=-1:0.01:2;y=exp(x)+x-4;plot(x,y,'color','blue')xlabel('x')ylabel('f(x)')ax…

Q: When is the integration method used?

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Q: arccos 2x dx 3.

A: We will use integration by parts. The solution is given below.

Q: 4. fx(1-x) dx

A: We can find the integration as below.

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Q: 4) dx (Use integration by substitution.) x' +1

A: As per our guidelines we can answer one question. please repost other Seperately

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Q: 1. | x cos x dx

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Q: Describe a first step in integrating x10 – 2r4 + 10x² + 1 -dx. 3x3

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Q: Use Integration by parts to solve: (3xsin(5x) dx

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Q: 5. x?e-3x dx

A: ∫x2e-3xdx

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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.