1. (4 x 10) (3.02 x 10)= 6.6×10 3x 10 3. 1.2 x 10 +5.35 x 10° D 2.

Q: (6) / zVF x² – 4 dx. Use TRIGONOMETRIC SUB STITUTION.

A:

Q: 9. z In(1 + x²) dx

A: As mentioned to solve only question number 9.Question number 9,Given,          ∫xln1+x2dx

Q: Sar en x² dx Given: Find: Formula o fe"du Sa"au

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Q: ,sinx cosx dx 7. E e А. 2e С. е — 1 D. 1 – e В. е

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Q: ? e tan(e") dx V sec? (e") – 7 ?

A: Solution is here

Q: 3 Given that 3. e dx = e° - e, use this result to evaluate 3ex + 4 dx.

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Q: 3e tanydr + (1– )sec?ydy = 0

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Q: et up a trigonometric ratio from ZH to solve for x. U 14

A: Trigonometric ratio

Q: S( sc x cot x + 5x4)dx

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Q: If 8 (x) = | sinx dx and g| |=3, then g (0) is equal to A 2 -2 D 4 B.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: の1) (のの) (めみ) Cn %3D Cnt = %3D antt San So,itis increa Sing. @dn=

A: dn=n32n! On simplification, we get dn=n32n·2n-1!=n22·2n-1! Now,…

Q: w = x18yz14 + sin(yz)

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Q: 4. SE cot x) csc° x) dx • (×) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: π 2 EK 4 cot4 x dx

A: Here, note that: ∫cot4x dx=∫cot2x cot2x dx=∫(cosec2x-1) cot2x dx=∫cosec2x cot2x dx-∫cot2x…

Q: sin(4(t – w)) y(w) du = 9t?.

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Q: Evaluate the given | coth - dx. 3 dz.

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Q: 2. I cosh ix dx

A: The given integral is ∫cos14xdx. Evaluate the integral.

Q: 2. cot2 x dx

A: Given- ∫cot2x dx To Find- The value of the above integral. Formula Used- cosec2θ=1+cot2θ

Q: Q.43) 2n S Icosx – sinx|dx =

A: Here we have to find solution of given integral

Q: 2. [ xsec’x cot xdx tamol svode se gniau s 3. ftsin2t dt

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

Q: Given: x² dx Find: Formula 1 o fe'du

A: Given problem:-

Q: "4 rseco sin 20 dp do d0 0. 0,

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Q: What is the value of ∫ 0 −1  x^3(4x^4−2)^4 dx? Enter your answer as an exact fraction if necessary.

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Q: | 7x°(x - 5)-4 dx

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Q: 14 S (sinti+(1+cost) j] -14

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Q: Ex: Salve the equation ofD-o Pelatermeth dy inzx

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Q: i?? cos(2t) dt csc(10t3)

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Q: When evaluated, | x sinh 3x² dx is equal to A. cosh3x? +C B. cosh3x? +C C. 3 cosh3x? +C D. 6 cosh3x…

A: we will let  3x2= t  to solve this question.

Q: 1. dy = %3D COSX cotytanx Cosy dr

A: Given- dy=1cotytanx-cosxcosydx To solve the given differential equation. Here we will arrange the…

Q: b) L{e" sin(3t)}

A: b) We need to evaluate the Laplace transform of the following expression e2tsin3t

Q: What is the value of ∫ 0 (top) −1 (bottom) x^3(4x^4−2)^4 dx? Enter your answer as an exact…

A: we use substitution method to integrate function..

Q: 4. s(x) 3D 2х * sec(х)

A: "Since you have asked multiple questions, we will solve ths first question for you. If you want any…

Q: If g (x) = sinx dx and =3, then g (0) is equal to A) 2 В -2 4 D

A: To find the solution.

Q: The value of cos jn is equal to O a. sinh 7 O b. jcosh 7 Oc jsinh 7 O d. cosh 7

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Q: Зп 4 |cot x|csc?x dx 4

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Q: 0 sin√xcos√x √x dx is equal to

A: To solve the given integral

Q: 2). EX+1 3t1a4 14. 13 What is the value of EX+1 for scoves I,

A: Given X1=1 X2=6 X2=3

Q: S sin* e de 4

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Q: Kindly sotve por : Dx (In | v | ) = Dx ((tan (3x) - In | 2x| + ( x³ - In | e|) - In | Inx | )

A: On differentiating Lhs: ddx(ln y)=1y.dydx on differentiating Rhs: ddx( tan(3x).ln|2x| +…

Q: To evaluate 1 dx 25+x2 the trigonometric substitution x = 5 sint

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Q: 7 dx = x3

A: ∫xndx=xn+1n+1+C1xn=x-n

Q: sinh (2xV1+x? dx

A: Given:         ddxsinh-12x1+x2          Apply differentiation rule:       sinh-1ux'=1ux2+1·u'(x)…

Q: V25-x² dx

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Q: x=sinht,y=cosht.

A: Dear student, since what is to find by using given parametric equations is not mentioned in the…

Q: d 53. cosh? (9 – 31) = –6 cosh(9 – 3t) sinh(9 – 3t) dt

A: Given derivative is ddtcosh29-3t.

Q: 4) SA tan?x dx ? А. — 1 В. 1 — С. 1/3 D. 프+ 1

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Q: Зп 4 |cot x|csc* dx 4

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.