Solve ∫ (from 0 to 101) of (1-x^00)x^49 wrt x

$$\int _ { 0 } ^ { 101 } ( 1 - x ^ { 00 } ) x ^ { 49 } d x$$

Evaluate

$$0$$

Solution Steps

Multiply 0 and 0 to get 0.

$$\int _{0}^{101}\left(1-x^{0}\right)x^{49}\mathrm{d}x$$

Calculate x to the power of 0 and get 1.

$$\int _{0}^{101}\left(1-1\right)x^{49}\mathrm{d}x$$

Subtract 1 from 1 to get 0.

$$\int _{0}^{101}0x^{49}\mathrm{d}x$$

Anything times zero gives zero.

$$\int _{0}^{101}0\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int 0\mathrm{d}x$$

Find the integral of 0 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$0$$

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.

$$0+0$$

Simplify.

$$0$$