Find a formula for the function represented by the integral 3t dt

Q: Evaluate the integral. x sec (3x) dx + C

A: Topic = Integration

Q: Find the formula for the function represented by the integral 1 -dt= 5t+1

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Q: The integral of the given function csc °x dx is equal to

A: Given,          ∫csc6xdx

Q: Evaluate the integral. бл t2 sin(2t) dt

A: We will apply ILATE rule hence t2 will be first function and sin2t will be second

Q: Evaluate the integrals ∫√t sin (2t3/2) dt

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Q: Evaluate the integral •5 sin(t)dt 6.

A: Given:∫65sintdt

Q: Evaluate the integral. t2 sin(2t) dt

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Q: Express each integral as a single integral.

A: Given: ∫29f(x)dx-∫49f(x)dx

Q: Determine an integrating factor and solve the followir xdy-ydx-(1-x')dx = o 1.

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Q: Evaluate the integral.

A:

Q: Compute this integral ∫( sqrt((e^x) +1) dx

A: To Compute this integral ∫( sqrt((e^x) +1) dx

Q: Find the indefinite integral. -0.02t dt = +C

A: It is given to find out the indefinite integral of f(x)=e-0.02t We know that ∫exdx=ex

Q: Evaluate the definite integral. t(5 – t)² dt

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Q: Find the indefinite integral ∫(ti + 3j) dt.

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Q: Evaluate the integral. ∫0 π/4 tan4 t dt

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Q: Find the answer to this integral:

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Q: Show that the integral -21/RC e dt has the value

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Q: Find the integral. (te -7e dt

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Q: Find the integral ( 5t sin(t) dt

A: We need to evaluate the following integralI= ∫5t2sintdt

Q: Evaluate the integral. (11 - t)/e dt

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Q: Evaluate the integral.

A: The integral ∫0π6tsin2tdt. We have to evaluate the value of this integral.

Q: Find formulas for the functions represented by the integrals.

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Q: Evaluate the definite integral. ∫0 π  Sec2 (t/4) dt

A: Given: ∫0πsec2t4dt

Q: Use the substitution formula to evaluate the integral. T/16 (1 + etan 4x) sec 2 4x dx 4e

A: Given that ∫0π161+etan4x sec24x dx ...........................(i) Substitute u= 4x  dudx=4 ⇒dx=du4…

Q: 1 -dt , find g'(2). V4 +t5 If g(x) =

A: Let's find.

Q: Find the indefinite integral dt t4 + 4

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Q: S x² √x²+4 dx

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Q: Evaluate the given definite integral using appropriate substitution: dx = 1– 2x A) 8ln(5/3) 2ln(5/3)…

A: From the given integration: I=∫2341-2xdx  ...1 Apply the substitution method to calculate the given…

Q: Use the substitution formula to evaluate the integral. Vx +1 dx B) 2/2 - 1 D) 3/2 - 3

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Q: Evaluate the indefinite integral. dt I (t + 13)8 + C

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Q: Evaluate the integral

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Q: Evaluate the integral. 8t 8 e S dt 1+ e 8t 8e 1+e 8t 8t dt =

A:

Q: Evaluate the integral: 5x sec (x) dx +C

A: Recall: ∫u.v dx = u∫v dx -∫dudx∫v dxdx   ( Product rule of integration) ∫ sec2x dx = tan(x)+C…

Q: dt 5+ t2

A: Given: ∫02t25-t2dt

Q: Find the indefinite integral ∫ t/√(1 − t4) dt

A: Given integral, ∫t1-t4 dt

Q: 5 dx 6. 2 x-2

A: We need to evaluate the following integral ∫25dxx-2

Q: Find the indefinite integral ∫(4t3i + 6tj − 4√tk) dt

A: We have to find indefinite integral: ∫4t3i+6tj-4tkdt We know the formula of integration, ∫xn…

Q: Evaluate the integral. V19 12) x dx 1

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Q: Consider the function Alt) = -2t + 10. Calculate At)dt by using 5.1 a graph and areas 5.2 a definite…

A: From the given function: ft=-2t+10 As we know that: The standard equation of the line…

Q: Evaluate the integral 3 sin(t)dt

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Q: Evaluate the integral. (Use C for the constant of integration.) 6x2 + 7x + 6 xp (x2 + 1)2

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Q: 3. If f(x) = [ 8+f dt ,find f'(1). .

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Q: 2. S", sec t dt -T/4

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Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: i +j- t3/2 k ) dt |

A:

Q: Find the indefinite integral ∫ t /(t4 + 25) dt

A: To evaluate the given integral

Q: Find the indefinite integral: (t3/2 + t-1/2 - 10t-1) dt

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Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

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.