What is the integral from 0 to x of sqrt(1+cos^2(t)) ?

The integral from 0 to x of sqrt(1+cos^2(t)) is sqrt(2)\E(x\vert 1/2)-sqrt(2)\E(0\vert 1/2)

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integral from 0 to x of sqrt(1+cos^2(t))

\int_{0}^{x} 1 + cos^{2} (t) d t

2 E (x ∣ \frac{1}{2}) - 2 E (0∣ \frac{1}{2})

Solution steps

\int_{0}^{x} 1 + cos^{2} (t) d t

Use the nonelementary integral:

\int 1 + cos^{2} (x) d x = 2 E (x ∣ \frac{1}{2})

= [2 E (t ∣ \frac{1}{2})]_{0}^{x}

Compute the boundaries:

2 E (x ∣ \frac{1}{2}) - 2 E (0∣ \frac{1}{2})

= 2 E (x ∣ \frac{1}{2}) - 2 E (0∣ \frac{1}{2})

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\int_{0}^{1} \frac{1}{x ^{6}} d x

\int_{0}^{l} x d x

\int_{1}^{l n (5)} e^{2 x + y} d y

What is the integral from 0 to x of sqrt(1+cos^2(t)) ?
The integral from 0 to x of sqrt(1+cos^2(t)) is sqrt(2)\E(x\vert 1/2)-sqrt(2)\E(0\vert 1/2)