4 Estimate dx using right endpoints for n = 3 approximating rectangles. 4 3 ·dx is approximately

Q: -0.5 Q3:Estimate √1 + x4 dx with an error 0.0001 ?

A: Given: f(x)=1+x4 To find: Value of integral ∫00.51+x4dx with an error 0.0001.

Q: (Tlog3(cosh z) + csch x) tanh x dx

A: Here we have to integrate the given Integral

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Sketch a graph of y = 8 on [- 5, 4] and use geometry to find the exact value of int -5 ^ 4 8 dx.

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Q: (a) 2-1 dx

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Q: Evaluate dy/dx at x = 2.5, correct to 3 significant figures, given y= (2x^2+3)/In 2x

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Q: 2. Use the composite trapezoidal rule with the step length h = 0.1 to evaluate dx I = 1+x2 and…

A: Composite trapezoidal and composite Simpsons 1/3rd rule

Q: 0.2 Approximate In|1 – 2x| dx to 3 decimal places

A: To evaluate the integral, use formula- I=u∫vdx-∫dudx∫vdx where u is the first function while v is…

Q: Find

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Q: E) INTEGRAL : 9.) S(5t3 + 2t? – 5t – 50)dt 10.) S(3x2 + 2x + 500)dx

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Q: Evaluate -dx using the appropriate steps and showing all appropriate work. 1+e

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Q: Write a differential formula that estimates the change in the surface area S= 6x of a cube when the…

A: Given that surface area of cube s=6x2and side length change from x0 to x0+dxsolution:x=x0  and…

Q: Integrate the following using ~2 x+1 2. dx

A: ∫12x+1xx-1dx

Q: 24. By Simpson's rule, evaluate Vi – 1/x dx with fiye ordinates

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Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Evaluate I ta tanh x ln(cosh x) dx.

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Q: 3. Evaluate dx. Hence find the value of sinx dx. Va -x)

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Q: 1 4x2 dx X.

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Q: 2 dx =

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Q: Select the correct answer. What is the value obtained by using left endpoints with n= 4 subintervals…

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Q: A. Use Simpson's rule to evaluate -dx ,by taking n= 4. Inx B. Find the length of the curve y = x…

A: Answer

Q: Find the approximate value of f 10. ' to 4 decimal places using e su

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Q: Use Romberg's method to compute dx 1+x? correct to 4 decimal places by taking h= 0.5,0.25 and 0.125.

A: AS PER OUR GUIDELINE WE ARE SUPPOSED TO ANSWER ONLY ONE QUESTION. KINDLY REPOST OTHER QUESTION AS…

Q: Find e dx approximately using Simpsons rule with n 10.

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Q: Use the Simpson's rule to estimate S, ex dx with n = 4

A: Consider the given integral ∫12ex2dx with n = 4. Simpson's rule is,…

Q: 3 Estimate the error if S10 (Simpson's rule with n = 10) was used to calculate sin(4 x) dx .

A: I=∫03sin4xdx Integrating it- I=-cos4x403=-cos124+cos04=1-cos124=0.0054

Q: 1+e* dx diverges 0.

A:

Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: Use the Trapezoidal Rule with n = 6 to ex approximate dx | 1 х Use the Simpson's Rule with n = 6 to…

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Q: d. x" tanh 1 dx VX %3D

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Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

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Q: Solve the following Exact DE using Method of Grouping. 3) () dx + () dy = 0 X-X y

A: Given:          2x-1ydx+x-x2y2dy=0     This is in the form of   Mx,ydx+Nx,ydy=0    where Mx,y=2x-1y…

Q: Evaluate 0, dx by dividing the interval into 10 equal parts 8х-5 by using Simpson's one - third…

A:

Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: Use the Simpson's rule to estimate e**dx with n = 4

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Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

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Q: Evaluate 1 dx, x = 0, x = 1 1- x

A: Using beta and gamma function.

Q: Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate…

A: The given integral ∫1e2ln x dx, three rectangles and left end points.

Q: -2 dx 0 (3+x)² 2

A:

Q: With n > 0, does x" dx get larger or smaller as n increases? Explain graphically.

A: Given: The given integral is ∫01xndx. Calculation: Use the integral formula, ∫xndx=xn+1n+1+C.…

Q: Sind dy forys(x) dx 3517X

A: y=(xx)3sin x

Q: dx by taking four 1+x Use Simpson's Rule to obtain the approximate value of intervals.

A: Given: ∫0111+x2dx Definition: If f(x) is continuous on [a, b] then Where, ∆x=b-an

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.