Consider the following integral dx After making the trigonometric substitution r = 3 sin 0, which does the integral become

Q: 1. Evaluate the following integrals. (a) (cot 0 + csc² 0 sin 20) d0

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Q: Given Tex+4 dx. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

A: Given ∫19x2+4dx Let substitute x=23tanθ. dxdθ=23sec2θdx=23sec2θ Substituting the value, we get…

Q: In the given equation , find the indefinite integral :-   See the equation as attached here

A:

Q: r2m 1 de 1 + 0.5 sin 0 2.

A: We have to find the value of definite integral.

Q: Consider S dx. Using trigonometric substitution, what is the integral fom in terms of 03

A: Given: ∫x2-9x3dx Using trigonometric substitution, we have to write the integral form in terms of θ.…

Q: After choosing the appropriate trigonometric substitution the integral dx, becomes

A:

Q: Evaluate the definite integral. sin(t) dt cos?(t)

A: The given integral is, Let u = cos t. Then, du = –sin t dt. The upper limit changes to u = cos(π/6)…

Q: After choosing the appropriate trigonometric substitution the integral 4 x² dx, becomes 4 cos (0)de…

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Q: Simplify the integral 1 dx using an appropriate trigonometric substitution. Va2 +4 Cos e do de sec 0…

A: Hence option (e) is correct.

Q: Consider the following integral dx - After making the trigonometric substitution x = 3 sin 0, which…

A:

Q: In the given equation , find the indefinite integral :-   See the equation as attached here

A: The indefinite integral is given as, I=∫sinθ sin3θ dθ Use the following trigonometric identity.…

Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)² esc…

A: Given Integral is ∫dx(x2+4)2Let's substitute x=2tanθDifferentiate with respect to x⇒dx=2sec2θ…

Q: (cot? 0 + csc² 0 sin 20) dð

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Q: Evaluate the following integral sin y dyde.

A: According to guidelines i solve first question only so kindly request you to repost the remaining…

Q: has the form - F(0)+ + C: What should be the value of e to make F(o)=0? The resulting integral of…

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Q: In the integral, cos?tsin2tat , the correct u using general power formula is; A cost B sin(2t) ©…

A: Given integral is ∫cos2tsin2tdt =  ∫cos2t(2sintcost)dt = 2∫cos3tsintdt Now taking u = cost…

Q: In the following equation/s, find the indefinite integral :-   see the equation attached here

A: We have to calculate the given integral   the given integral is

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. dx…

A: We have to find the integral

Q: To solve J- -dx using a suitable trigonometric substitution, the integral can be rewritten as…

A: We are given the Integral : ∫14+9x2dxLet x=23tan θ⇒dx=23sec2θ dθ∫14+9x2dx=∫14+923tan θ223sec2θ dθ…

Q: The given integral (cos?r – sin²x) dx is equal to

A:

Q: After choosing the appropriate trigonometric substitution the integral 4 x dx, becomes

A: Apply trigonometry property and solve it

Q: 1 dx becomes: Using a trigonometric substitution, the integral x* V1-x? Select one: Jcsc* e de Sante…

A:

Q: If you are going to evaluate the integral S V1 - 7w-dw using trigonometric substitution, the answer…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: In the given question as follows , find the trigonometric integral :-   see the equation as attached…

A: Given: I=∫sec4x2dx For evaluating given integral, we substitute tanx2=t…

Q: When the integral is evaluated by trigonometric substitutio exV4 – e2x the integrand is transformed…

A: Given- To do - Multiple Choice Question with options below,

Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

A: Given integral is ∫x2-x2-1 dx.

Q: Using substitution with u= sin(2x), the definite integral | 4 sin³(2x)cos(2x)dx is equivalent to (A…

A: The given integral is ∫0π4sin32xcos2xdx.

Q: cos e d0 Jo 1+sin? A 2

A:

Q: Vr2 – 3 dx

A:

Q: The value of the integral sin() dy dz is

A:

Q: S sin y cos('/2) dy

A: ∫sinycosy2dy

Q: dx 4 2 +3

A:

Q: Consider the following integral d.r After making the trigonometric substitution ar = 3 tan0, which…

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Q: Find the following integral. | tan? x sec* x dx

A:

Q: Evaluate the following integrals. 4 (a) (cot? 0 + csc? 0 sin 20) d0

A: definate integration

Q: In the given question as folows , use trigonometric substitution to find or evaluate the integral :-…

A:

Q: Consider the following integral dr After making the trigonometric substitution r = 3 tan0, which…

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Q: S The integral S x dx x²+√√x²-1-1 sece tane de sece - 1 sec²0 do 1+tano cose dᎾ 1 - sino sine de 1 +…

A:

Q: Given dx. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

A: Given: ∫19x2+4dx Let I= ∫19x2+4dx To solve this we need to the trigonometric substitution

Q: If you are going to evaluate the integral f dx using trigonometric substitution, the answer is 2(tan…

A:

Q: For the given integral dx sin-cot- 2 2 what is u?

A: Take u=x/2 then integrate it

Q: Given SV-x* + 4x + 5 dx. Using trigonometric substitution, what is the integral form in terms of 8?…

A: Trigonometric identities: sin2θ+cos2θ=1cos2θ=1+cos2θ2 If an expression is x2+bx, then we need to add…

Q: Find the value of the following integral: cos2r dx,a>0 71+a

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Q: The integral O x dx can be transformed to which of the following using trigonometric substitution?…

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Q: The best substitution to use for the integral sin z V1+ cos z dx

A: when we substitute, u = 1 + cosx then the value of du = - sinx dx

Q: Evaluate the following trigonometric integral sin? d0. 5+4cos 0 “o.

A: Let the given integral be y -y = ∫02π sin2θ5+4cosθ dθ           .............(1)Given,z = eiθ…

Q: The integral / sin²xcos?xdx is equal to M – cosN) dx' what is M and N? (1- M= N=

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Q: Use the trigonometric substitution r 2 sin 0 to compute the integral -2 VA – r² dx

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Q: After choosing the appropriate trigonometric substitution the integral | x2 - dx, becomes

A:

Q: Which expression represents the midpoint approximation M3 to the integral r12 sin (/æ) dx?

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.