4. Integrate COs x dx

Q: Evaluate the integral.

A:

Q: 211 211 cos nx dx= [cos %3D %3D nx cos nx dx =0.

A:

Q: π/2 cos² x dx

A: This question can be solved using the concept of properties of definite integrals.

Q: Evaluate ]e * cos (7x) dx. Seex cos (7x) dx = %3D

A: Explanation of the answer is as follows

Q: (In x) dx CoS

A: we have to find the integral of ∫cos(lnx)dx

Q: Integrate the following: 1. 1+x² dx (1+x)³ 2. sin5 cos5 x dx

A: here we have to integrate the given function.

Q: 6. (a) cos 2x dx; u = 2x

A:

Q: 5) Find if y = (cos h x)* dx

A:

Q: Compute d/dx  sin-1 (x/x+1)

A:

Q: nasin(hx) cos(bx)dx

A:

Q: 1. Integrate: e3x cos(x) dx

A:

Q: 3+9sin' x Evaluate dx using suitable technique. cos x

A:

Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: J cos 3x cos 4x dx :

A:

Q: 2. Vsin 3x cos 3xdx

A: Given: I=∫sin3xcos53xdx For evaluating given integral, we substitute sin3x=t…

Q: 3. Explain graphically: cos x dx = 0.

A:

Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: (4) Evaluate cos (2x) -dx. (x² + 1)² 8.

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

A:

Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: 4) Find when y? - x2 + cos(x + y) = 0 %3D dx

A:

Q: x fare cos = dx 2

A: Indefinite Integration

Q: 4. ſ cos xesinx dx

A:

Q: determine dy/dx if xy = ecsch(x)+πcos(0)

A: Given, xy = ecsch(x)+πcos(0)

Q: 1. § e sin 4x cos 4x dx 2.5 dx Se-2x dx %3D

A: 1) Given:                ∫esin 4x cos 4x dx Apply u-substitution: u=sin 4x⇒du=4 cos 4x dx…

Q: Take the derivative of this integral.

A: Given

Q: find dy. = cos (x2)

A: Given- y=cosx2 To find- The value of dydx. Formula used- ddxcosx=-sinx.

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: b) S. cos x cos 7x dx

A:

Q: 9. . 2 CoS cos rsin?x dx. 10. 2 sinºx dx

A:

Q: Find if y%3D cos (2x)+ 2еж: dx dy

A:

Q: 3x d. Evaluate dx COS cos (3t – 1) dt

A:

Q: 3z cos(z)dz

A:

Q: y = sin(3x) + cos(0.5x)

A: Given: y=sin(3*x)+cos(0.5*x) We have to determine the value of y,where x varies from 0 to 2pi in an…

Q: Evaluate J2 e* cosx dx 0.

A: To evaluate: The definite integral ∫0π2ex·cos x·dx. Concept used: Integration by parts:…

Q: 5 Find *: (a) y = cos(11x + 2x) dy

A:

Q: 1 dx 3 sin x+4 cos x+3

A:

Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: Find Se2= cos(x)dx.

A:

Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: 1. x2 cos 2x dx

A: The given integral is: ∫x2cos 2x dx

Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

A:

Q: CM 2: S cos"x sinx dx

A:

Q: Integrate: S V1 – cos x dx

A:

Q: 1. " x² cos 2x dx

A: (1) We need to evaluate the following integral ∫0πx2cos2xdx

Q: Compute cos(4x) -∞ (x²+2x+2)' dx.

A:

Q: 4x Cos x dx b.

A: Given :

Q: X cos (3x) dx,

A:

Q: dy = 4 cos 4x dx

A: The given differential equation is dydx=4cos4x. We can solve this differential equation using…

Q: 7. Find (a) y = (x* + 5x) cos 5x %3D dx

A: We can find the derivative using product rule as below