eP(x) (1+ tan²x)dx

Q: Q4: Using Fixed-Point Method, find the Positive Root of the following equation: Sin x = 5.x - 2 ,…

A: We have to find positive root by using fixed point method.

Q: evaluate the integral.

A:

Q: y=Arccos (x²)

A:

Q: 30. Solve using trigonometric substitution S - (1+x² dx

A: Here I am attaching image so that you understand each and every step.

Q: dx 2. e2x+1

A: ∫dxe2x+1let ex=tan ydifferentiate O.B.Sexdx =sec2y dy∫1tan2y+1×(sec2y dytany)

Q: cosxsin?xdx Solve using algebraic substitutionf V1+sinx

A: We have to find Integration using algebraic substitution.

Q: 3. sin°x dx 9. S coSX

A:

Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

A:

Q: (2xy-sinx) dx + (x² - cosy) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: Find the genereal solution. NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS (D2 + 1)y = sinx

A:

Q: | What is sin²(20) d0?

A: From the given problem:   I=∫0π4sin22θ dθ...(1)   As we know that:   sin2θ=1-cos2θ2=121-cos2θ So,…

Q: Sx2.- cos³ x-5 du 1-sin? x

A: Evaluation of the integral, bu using integral by parts

Q: y = x^Arctan *(x4)

A: We have to solve derivative

Q: 6. [(2- tanxsecx) dx

A: The solution is given below

Q: Solve the equation for x.

A: Given arctan (2x-5)=-1, To find x,

Q: dx x2 — 2х — 4

A: I=∫dxx2-2x-4=∫dxx2-2x+1-5=∫dx(x-1)2-52

Q: y" - y = xe + sinx

A:

Q: 1. x*dx 2 3 (16–x³) 2 X-

A:

Q: SVx-2 Using substitution method to solve dx? Please identify u and find du. Then solve problem. x+1

A:

Q: r2+vZ 1. =dx |4x – x²

A:

Q: Find the limo (cos x) = Show your complete solutions. No shortcuts.

A: Given,  limx→0cos x1x2

Q: )xsin(x?) dx

A: The given integral is: ∫0πx sinx2dx To integrate this, consider x2=t  .... (1) On integrating both…

Q: y = 2 sin 3x 1+3cos2x

A: We are given  y= 2sin3x/(1+3cos2x)  We have to compute y'.    Before computing y', let us first see…

Q: y = Arctan (2x)

A:

Q: Q: Solve y+8= Cos (x) ナ3sin(2x)

A: Given: y''+y=cos x+3 sin 2xCE: m2+1=0⇒m=±iCF: e(0)x( Acos x +B sin x)=Acos x +B sin x

Q: x*dx 1. - (16-x)

A: The solution of the problem is given in the next step.

Q: V2r – x² dx

A:

Q: 1/2 6. dx, x = sin e VT

A:

Q: 2 sin (csc 2x) dx

A:

Q: 4e2x S sin(e²x) dx

A:

Q: y = c sinx

A: It is known that ddxsinx=cosx and ddxcosx=sinx. We need to eliminate the arbitrary constant: c from…

Q: Solve tanh(x) sech (x) dx

A:

Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A:

Q: 8. dx Vx² -9 2 X

A:

Q: Solve by any two methods if it possible if not explain why not. (D + 8D2 -9)y = coshx – sin?x

A: Given differential equation is D4+8D2-9y=coshx-sin2x Now auxiliary equation is…

Q: L {2-e2t+4t²-5 sin (√2t) + cosh (t)}

A:

Q: S- d.x (sin3r2)?

A: To find: ∫2xsin3x22dx

Q: 3. 3x²y dx - (x³ + y³)dy = 0, y(1) = −2

A:

Q: 9. dx V25+x2

A:

Q: dx e 2x+1

A:

Q: A. Solve: tanh(1 - i). Express your answer in rectangular form.

A: We use the formula ? sin(x+iy)= sinhx cosy +i coshx siny  ? coshx(x+i y) = coshx cosy +i sinhx siny…

Q: 3 x²(x³ + 1)īdx

A: Given : ∫x2x3+134dx

Q: dx e2X+1

A:

Q: ~In 3 2. x²e-*dx 0.

A: To determine the value of the integral.

Q: y" – 7y' + 6y = 2 sin

A: According to the given information, it is required to determine the general solution of the given…

Q: et dx (9 + e2¤)

A: Integration   by subsitution technique

Q: Kindly solve using trigonometric substitution. Show detailed solution. y² + 4 dy y

A: We use Trigonometry substitution method

Q: 3 dx 3 X´ – 1

A:

Q: dx x= 2 tane 1/2 X2VX2 +4

A:

Q: solve for general solution y''''=5 sin x

A: The given equation is y''''=5sin(x). The given equation is equivalent to D4y=5sin(x). Consider the…