Indefinite integral integral sin^3(x) dx = 1/12 (cos(3 x) – 9 cos(x)) + constant Expanded form of the integral 1/12 cos(3 x) – (3 cos(x))/4 + constant Series expansion of the integral at x=0 -2/3 + x^4/4 + O(x^6) (Taylor series) Definite integral over a half-period integral_0^pi sin^3(x) dx = 4/3~~1.33333 Definite integral mean square integral_0^(2 pi) (sin^6(x))/(2 pi) dx = 5/16 = 0.3125
Indefinite integral integral sqrt(x) dx = (2 x^(3/2))/3 + constant
Indefinite integral integral sqrt(x) dx = (2 x^(3/2))/3 + constant
Indefinite integral integral 1 sqrt(x) dx = (2 x^(3/2))/3 + constant
Input interpretation law of sines Alternate names sine law | sines law Basic definition For general triangles, a formula relating the ratios of sines of angles to the opposite side lengths. Detailed definition Let a, b, and c be the lengths of the legs of a triangle opposite angles A, B, and C. Then the law of sines states that a/(sinA) = b/(sinB) = c/(sinC) = 2R, where R is the radius of the circumcircle. Related topics generalized law of…
Indefinite integral integral x sin(x) dx = sin(x) – x cos(x) + constant Alternate form of the integral -1/2 e^(-i x) x – 1/2 e^(i x) x + 1/2 i e^(-i x) – 1/2 i e^(i x) + constant Series expansion of the integral at x=0 x^3/3 – x^5/30 + x^7/840 + O(x^8) (Taylor series) Definite integral integral_0^pi x sin(x) dx = pi~~3.14159
Indefinite integral integral 1 cos(x) dx = sin(x) + constant Alternate form of the integral 1/2 i e^(-i x) – 1/2 i e^(i x) + constant Series expansion of the integral at x=0 x – x^3/6 + x^5/120 + O(x^6) (Taylor series) Definite integral integral_0^(pi/2) cos(x) dx = 1 Definite integral mean square integral_0^(2 pi) (cos^2(x))/(2 pi) dx = 1/2 = 0.5
Input i sqrt(1) Result i
Indefinite integral integral 1 sqrt(x) dx = (2 x^(3/2))/3 + constant
Indefinite integral integral cos^3(x) dx = 1/12 (9 sin(x) + sin(3 x)) + constant Expanded form of the integral (3 sin(x))/4 + 1/12 sin(3 x) + constant Series expansion of the integral at x=0 x – x^3/2 + (7 x^5)/40 + O(x^6) (Taylor series) Definite integral integral_0^(pi/2) cos^3(x) dx = 2/3~~0.666667 Definite integral mean square integral_0^(2 pi) (cos^6(x))/(2 pi) dx = 5/16 = 0.3125