Example 1: Using the Riemann sum technique from section 5.2, evaluate , x3 dx. Example 2: Use the Fundamental Theorem of Calculus part 2 to evaluate f, x3 dx.

Q: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88    0.75…

A: Given: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88…

Q: Example for unboundedness Min -2₁-3x2 2₁-22₂54 -2₁ + x₂ 5 3 x2 x₁, x₂ > 0 s.t

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Q: 1. Which is equal to cos ? cos O sin * O sin O Cos 품 27 COS

A: topic - trigonometric ratios

Q: 9. Simplify sec² x - 1 sec² x

A: secx=1cosxI=sec2x-1sec2xsin2x+cos2x=1

Q: Let x + 3 f(x) x + 6 f-'(- 10) =

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Q: 1f \ x | < 1 and 1= x < < 1; then: 2 ₂ F₁ (a, b ; c ; x ) = (1 − x)¯ª₂ F₁ [a, c − b; c; X _— — ₁) X-

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Q: Let f(×)=-4×,h(×)=-×+5 find (foh)(6)

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Q: Solve for Fourier coefficient, {6" ax 02x2n T >x 22n sin x f (x) =

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.