Solve ∫ (from x to x ^ 2) of sintdt

$$\int _ { x } ^ { x ^ { 2 } } \sin t d t$$

Evaluate

$$-\cos(x^{2})+\cos(x)$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \sin(t)\mathrm{d}t$$

Use \int \sin(t)\mathrm{d}t=-\cos(t) from the table of common integrals to obtain the result.

$$-\cos(t)$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$-\cos(x^{2})+\cos(x)$$

Differentiate w.r.t. x

$$2x\sin(x^{2})-\sin(x)$$