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Popular >

integral from 1 to x of 2-t

Solution

\int_{1}^{x} 2 - t d t

Solution

2 x - 2 - \frac{x ^{2} - 1}{2}

Solution steps

\int_{1}^{x} 2 - t d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{x} 2 d t - \int_{1}^{x} t d t

\int_{1}^{x} 2 d t = 2 x - 2

\int_{1}^{x} t d t = \frac{x ^{2} - 1}{2}

= 2 x - 2 - \frac{x ^{2} - 1}{2}

Popular Examples

integral from-pi to pi/2 of cos(nx)

\int_{- π}^{\frac{π}{2}} cos (n x) d x

integral from 0 to 0.5 of xcos(pix)

\int_{0}^{0.5} x cos (π x) d x

integral from 2 to 3 of x+3

\int_{2}^{3} x + 3 d x

integral from 4 to 6 of (5/3 x-5)

\int_{4}^{6} (\frac{5}{3} x - 5) d x

integral from-1 to 5 of 4x^3-3x^2+1

\int_{- 1}^{5} 4 x^{3} - 3 x^{2} + 1 d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to x of 2-t ?
The integral from 1 to x of 2-t is 2x-2-(x^2-1)/2