{eq}\displaystyle \int \sin (2x) + \cos(3x) dx = {/eq}___ Fundamental Theorem of Calculus: The fundamental theorem of calculus finally reveals to us the relationship between integration and differentiation: they are inverse processes of one another. So an integral is really the deri...
Evaluate the integral of sin 2x cos 2x dx. Evaluate the integral. integral_0^{pi / 2} {cos x} / {(5 + sin x)^2} dx Evaluate integral of sin (5x) dx Evaluate the integral: sin 3x cos 7x dx? Evaluate: integral 24x sin x dx. ...
Write down the integral of the following (i)x2/3+1(ii)(3√x+5x4) View Solution Find an antiderivative (or integral) of the following cos 3x (ii)3x2+4x3(iii)(ax+b)2(iv)sin2x−4e3x View Solution Integrate the following :sinxsin(cosx) ...
Evaluate the integrals. (a) \int_{0}^{1} (3x^3-5) cosx dx (b) \int_{0}^{e-1} ln(x+1) dx Evaluate the indefinite integral. Integral of (cos x)/(sin^2 x) dx. Evaluate the indefinite integral. (Use C for the constant of integration.) Integral of (...
Substitute backu=xt=x1(−cos(xt)) Simplify=−x1cos(xt) Add a constant to the solution=−x1cos(xt)+C Popular Examples Frequently Asked Questions (FAQ) What is the integral of sin(xt) ? The integral of sin(xt) is -1/x cos(xt)+C...
Evaluate the definite integral: \int_{0}^{\pi/2}(2 cos(x)+7sin(x))dx Evaluate the integral \int \frac{e^{5\sqrt z{\sqrt z} \,dz Evaluate the integral. \int_{1}^{2}((5 - 3t)\boldsymbol{i} + 5\sqrt{t}\boldsymbol{j})dt Evaluate the integral: integral of ...
let 3x = u => 3 dx = du (after derivation) or dx = 1/3 du => ∫ sin 3x dx turned as∫ sin u X 1/3 du or 1/3 ∫ sin u du which is 1/3 (-cos u) + C, where C= constant of integration Substituting values again, we get ...
{-x})/x)dxd(x(e−x))derivative of f(x)=(x-2)/(x^2-2x-3)derivative off(x)=x2−2x−3x−2tangent of f(x)=-3/2 x^2+3x+3tangent off(x)=−23x2+3x+3derivative of (e^x-2)^{1/2}derivative of(ex−2)21integral of (xsin(2x))∫(xsin(2x)...
(sinx+cosx)2 dx=∫0π4lnsin(2x)sin2(x+π4) dx=x→π4−x∫0π4sec2xlncos(2x) dx=∫0π4lncos(2x) dtanx=limx→π4lncos(2x)+2∫0π41−cos(2x)cos(2x) dx=−π2+limx→π4ln[1+sin(2x)]=−π2+ln...
Evaluate the integral. Integral (1/2)^{sin (x)} cos x dx Evaluate the integral: integral of 3/(16 + x^2) dx. Evaluate the integral: integral x^2 cos (x) dx. Evaluate the integral. Integral of (2x + 7) dx from 3 to 5. ...