Solve ∫ (from 0 to x ^ 2) of sinsqrt{7}dt

$$\int _ { 0 } ^ { x ^ { 2 } } \sin \sqrt { 7 } d t$$

Evaluate

$$\frac{2308033129306663x^{2}}{50000000000000000}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\int_{0}^{x ^ {2}} {0.04616066258613326} dt$$

Evaluate the indefinite integral first.

$$\int 0.04616066258613326\mathrm{d}t$$

Find the integral of 0.04616066258613326 using the table of common integrals rule \int a\mathrm{d}t=at.

$$\frac{2308033129306663t}{50000000000000000}$$

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.

$$0.04616066258613326x^{2}-0.04616066258613326\times 0$$

Simplify.

$$\frac{2308033129306663x^{2}}{50000000000000000}$$

Differentiate w.r.t. x

$$\frac{2308033129306663x}{25000000000000000}$$