Let s(t) = E-„8(4t – 4kn), where k is an integer. The result of the integration s(t)stnc(t)dt is A. 1 ! B. C. D. m8(24)

Q: let w=ln(x2+y), x= 2t, y=4-t. compute dw/dt a) using the Chain rule, draw corresponding tree diagram…

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Q: Find the weighted integration distance (f,g) = f* f(x)g(x)w(x) da between the given polynomials.…

A: Step 1: Step 2: Step 3: Step 4:

Q: f(9) = – 10 and | f(t) dt = - 7 then: I· f'(x) dz 0.

A: This question can be solved by using the concept of integration by parts.

Q: d (t2 sec(t)3' E Please select file(s) Select file(s)

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Q: Let X ~ N (0, 1). Demonstrate that E (X)=0 and V (X)=1.

A: To demonstrate that E(X)=0 and V(X)=1 for a standard normal distribution X∼N(0,1), we need to…

Q: Suppose X~N(180,15), and Z~N(0,1). Then x = 185, is equivalent to z = ______. (Round your answer to…

A: Given that, x~N(180,15)  Mean = 180  standard deviation = 15  We know that z-score is given by,…

Q: et d Calculate dt \e +1) ()

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Consider the function | dt, defined in [-2, +). Find the local max/min of f(x).

A: Local maxima and minima  Use lebnitz theorem for differentiation

Q: Q14) (A) (t) sin(2t) e-st dt = (B)e- e- (C) se-F. s2+4 (D) 2e-8. 82 +4 (E) e

A: The integralFrom the shifting property, we haveHere

Q: 2 2et 5 Let 7(t) 5, Evaluate the definite integral. %3D 13 | F(t)dt = ( 6.

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Q: f (t) =1*b +acosh 21 + bsinh 21 a+b

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Q: et dt 3/2 +8 e' +

A: Given integral is, ∫ete2t+8et+732dt. It is integrated by applying u-substitution method, Substitute…

Q: Integrate: +C 16t6 t4 [√16 dt

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Q: 4. (y? – 3)ž dy

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Q: 3t+4 dt 1 (t+1)(t+2) 2.

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Q: B/Fnd Z transform z(n) = " (n) – u(n-5))

A: Given equation: x(n)=15nun-un-5

Q: Evaluate S(ti + tj + t°k)dt = i+ j+ k.

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Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: Evaluate (z – i) dz where C:y(t) = VE² +1 + it³, 0<t < 1

A: We have to find ∫Cz-idz where C: γt=t2+1+it3, 0≤t≤1

Q: find ,(t³i+7j+(t+ 1)k)dt

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Q: (h) S (z+1)(z*+2=+5)dx (Hint: consider f(2) logz (z+1)(2+2z+5) in a key-hole contour.) %3D

A: In order to solve this integral we need to divide it into partial fractions and then integrate…

Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

Q: If B(p,q) = S, tP-'(1– t)9-1 dt then prove that %3D 1 B(p = 1, q + 1) = 2 t2p+1(1– t²)ª dt.

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Q: A manufacturer of lightbulbs wants to produce bulbs that last about 700 hours but, of course, some…

A: Since derivatives of F(t) represent the rate at which the fraction F(t) of burnt out bulbs increase…

Q: where a = If loga z= dt, then r= exp

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Q: 3 Let r(t) = · (1 ²³₁,e², Vt-2). t-1 √ F(t)dt = { Evaluate the definite integral.

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Q: Varlx) = µ(t) – HC)

A: Here use variance definition using  moment

Q: Let X ~ NB(r, p). Show that E(X*) =-E(Y – 1)*-1 where Y ~ NB(r+1, p). а. b. Use this result to find…

A: It is given that:

Q: Solue the differential equator da t- 2Q=4, Q6)=100 dt 10t2t

A: Given : The differential equation is : dQdt+210+2tQ=4. and Q(2)=100 We have to find the solution for…

Q: 4. Let (1, X (jw) = 10, 0 < x ≤1 otherwise Find x(t) using the inverse continuous-time Fourier…

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Q: Suppose X~N(165,16), and Z~N(0,1). Then x = 173, is equivalent to z = ______. (Round your answer to…

A: Given: X~N(165,16) μ=165σ2=16Thus, σ=σ2=16=4 And X=173

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.