f ( x ) = sinh 2x;  1

Q: Integrate the following function by using trapezoidal rule. 142*dx

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Q: f(x)=square root of x from a=3 to b =6 area under curve

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Q: The velocity of a car, in ft/sec, is v(t) = 5 t for t in seconds, 0 <t < 6. (a) Use At = 2 to give…

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Q: Estimate

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Q: Use the function y=2x from x=0 to x=1 and n equal subintervals with the fuction evaluated at the…

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Q: Q1- Prove that coth x = 2 csch 2x + tanh x %3D

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Q: Using Legendra polynomia lsFind 9quadratic least-square approximation For cosh Cx)

A: We have , fx = coshx We know that , the quadratic approximation of  least square polynomial is given…

Q: Graph the function f(x)=-5x^2-6  On [0,4] And find the average value over the interval

A: We have to find average value

Q: Determine the area, in square units, bounded above by f(x)=−x^2−10x−16 and g(x)=2x+16 and bounded…

A: Given that fx=-x2-10x-16gx=2x + 16 The objective is to find the area of the region which is bounded…

Q: Find the area under the curve  y= (2x2 - 7) / (sqrt(x)) ,   16 <= x <= 20

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Q: メ+」 dx xーメ de = 分海 2 3 ニ メ (x+° X4+が X3

A: Part(1) We have ∫x2+1x3-xdx Now,  x2+1=133x2-1+43 Hence, we get:…

Q: the function f(x)=1/2x^2+1 find the area under the curve of f(x) from 1 to 4 using upper and lower…

A: Given the function is: f(x)=1/2x2 +1 We need to find the area under the curve of f(x) from 1 to 4…

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.