a(cos2x) sin(x-) TC 1. f(x) = tanx 4. What values should a and b take for the function fx) to be continuous in the interval (0,90)?

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A: Given curve: fx=2cosx sin2x

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A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: 14. S 5 sin 3x cos 3x dx 15. ſ tan? Ode

A: We can solve the given integral as follows:

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Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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A: Given- ∫sintanxcos2xdx To find- The value of the above integral. Concept Used- The above integral…

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

Q: 3) If f is continuous everywhere and | f(x) dx = 6, find sec" 2x · f(tan 2x) dx.

A: d/dx(tanx)=sec^2x Tan (pi/4)=1

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A: Here we want to perform the given integral according to each of the methods mentioned.

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A: Given query is to find the intersection.

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Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

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A: the given implicit function is: 2+4x=sinxy2

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A: Given that: tan3x

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A:

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A: Solution:- Use the first two non-zero terms to estimate ∫01sinx2dx

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A:

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A: Given that the function is       f(x) = sin(3 ln(x)) We have to differentiate the the function f(x).

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A: Solution is in step 2

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A: We have to find

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A: From the given data:

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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.