integral sinx dx

If u is a function of x, we can use the following formula to evaluate an integral. f dx = (f/(du/dx)) du Using the Formula Use of the formula is equivalent to the following procedure: 1. Write u as a function of x..

The process of finding functions whose derivative is given is called anti-differentiation or integration. ∫ f(x) dx = F(x) + C The function F(x) is called anti-derivative or integral of the function f(x) and C is called Constant of integration..

Put g(x) = t Differentiating g(x) with respect to t, we have g'(x) dx = dt F(t) + C F(g(x)) +..

Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(..

Evaluate the definite integral ∫ 0 2 (5 + x ) dx . => 1 or 0 or 12 or - 12 or 2..

Evaluate the integral by using the reduction formulas. ∫ tan 5 (3 x ) dx => IV or I or III or II or V..

Evaluate the improper integral ∫ 0 ∞ cos x dx if it is convergent. => 1 or 0 or 2 π or divergent or - 1..

Evaluate the integral by using reduction formulas. ∫ sin 5 ( x + 2) dx => cos 5 (x + 2) + C or - 1 / 5 sin 4 (x + 2) cos (x + 2) - 4 1 5 sin 2 (x + 2) cos (x + 2) + C or - 1 / 5 sin 4 (x + 2) cos (x + 2) + 8 1 5 cos(x + 2) + C or 1 6 sin 6 (x + 2) cos (x + 2) + C or ..

Calculate the trapezoidal approximation T n to the integral ∫ 0 4 x dx . Using 4 subintervals. => 10 or 8 or 5 or 16..

Evaluate the definite integral ∫ -1 1 ( x 3 - 2 x ) dx => 1 or - 1 or 0 or - 2 or 2..