What is the integral of sin (x) dx from 0 to 2pi? - Socratic
Jul 4, 2015 · Using the definition of the integral and the fact that sinx is an odd function, from 0 to 2pi, with equal area under the curve at [0, pi] and above the curve at [pi, 2pi], the integral is 0. This holds true for any time sinx is evaluated with an integral across a domain where it is symmetrically above and below the x-axis. int_0^(2pi) sinxdx = [-cosx]|_(0)^(2pi) = -cos2pi - (-cos0) = -1 - (- 1 ...
Integration of int e^sin(x) dx? - Socratic
Feb 25, 2018 · Explanation: There's really no way to integrate this. The way to integrate is to think "this is the derivative of what?" Since your original equation is. esin(x) You can't actually apply this, because it would mean: ∫esin(x)dx = − esin(x) cos(x) This isn't the case, however, because this becomes a quotient rule, which leads to a much more ...
How do you integrate #sin(x)cos(x)#? - Socratic
Aug 2, 2016 · Answer link. Depending on the route you take, valid results include: sin^2 (x)/2+C -cos^2 (x)/2+C -1/4cos (2x)+C There are a variety of methods we can take: Substitution with sine: Let u=sin (x). This implies that du=cos (x)dx. Thus: intunderbrace (sin (x))_uoverbrace (cos (x)dx)^ (du)=intudu=u^2/2+C=color (blue) (sin^2 (x)/2+C Substitution ...
How do you find the integral of sin^3[x]dx? - Socratic
Mar 19, 2016 · Putting it all together, we get our final result: ∫sin3(x)dx = ∫sin(x)dx −∫sin(x)cos2(x)dx. = − cos(x) + 1 3cos3(x) +C. Answer link. intsin^3 (x)dx = 1/3cos^3 (x)-cos (x)+C intsin^3 (x)dx = intsin (x) (1-cos^2 (x))dx =intsin (x)dx - intsin (x)cos^2 (x)dx For the first integral: intsin (x)dx = -cos (x)+C For the second integral, using ...
What is the integral of int sin^5 (x) dx? - Socratic
Mar 4, 2018 · What is the integral of #int sin^5 (x) dx#? Calculus Introduction to Integration Integrals of Trigonometric Functions. 1 Answer
What is the integral of #sin^6(x)#? - Socratic
Apr 28, 2018 · What is the integral of #sin^6(x)#? Calculus Basic Differentiation Rules Chain Rule. 1 Answer maganbhai P. ...
How to integrate arc sin x dx? - Socratic
Mar 4, 2016 · Answer link. intarcsin (x)dx = xarcsin (x)+sqrt (1-x^2)+C We will proceed by using integration by substitution and integration by parts. Substitution: Let t = arcsin (x) => x = sin (t) and dx = cos (t)dt Then, substituting, we have intarcsin (x)dx = inttcos (t)dt Integration by Parts: Let u = t and dv = cos (t)dt Then du = dt and v = sin (t) By ...
What is the integral of sin(101x)sin^99(x)dx? - Socratic
1 Answer. Cem Sentin. Jan 11, 2018. ∫sin(101x) ⋅ (sinx)99 ⋅ dx = 1 100sin(100x) ⋅ (sinx)100 + C.
What is the integral of int (sinx)/(cos^2x) dx? - Socratic
Mar 13, 2016 · Explanation: We should try to use substitution by setting u = cosx, so du = − sinxdx. This gives us the integral: ∫ sinx cos2x dx = − ∫ −sinx cos2x dx = −∫ 1 u2 du = − ∫u−2du. From here, use the rule. ∫undu = un+1 n + 1 + C. Thus,
How do you integrate x^2(sinx)dx? - Socratic
Jul 26, 2016 · Explanation: Use integration by parts, which takes the form: ∫udv = uv − ∫vdu. For ∫udv = ∫x2sin(x)dx, we let: u = x2 ⇒ du dx = 2x ⇒ du = 2xdx. dv = sin(x)dx ⇒ ∫dv = ∫sin(x)dx ⇒ v = − cos(x) Thus, substituting these into the integration by parts formula, we see that: ∫x2sin(x)dx = −x2cos(x) − ∫(− 2xcos(x))dx ...