# How do I compute an integral (sum, product)?

It is easy to compute a definite integral:

∫(sin(x), x, 0, π)

1.99999999984

Hint: To type the integral sign, ∫, type “\int” followed by space or a punctuation character. In this case, ( will do.

Hint: To type π, type “\pi” followed by space or a punctuation character. In this case, ) will do.

Hint: Instead of `∫`

, you may use the synonym `integrate`

.

Similarly, you can compute sums and products:

∑(1/k!, k, 0, 100)

2.71828182846 (=e)

∑(2^k⋅k!^2/(2⋅k + 1)!, k, 0, 100)

1.57079632679 (=π/2)

∑(1/(1 + Fibonacci(2⋅n + 1)), n, 0, 100)

1.11803398875 (=√5/2)

Hint: To type the n-ary summation symbol, ∑, type “\sum” followed by space or a punctuation character. In these examples, ( will do.

Hint: Instead of `∑`

, you may also use the synonym `sum`

.

Hint: You can also sum vectors or matrices:

∑(❨1, k, k^2, k^3, k^4❩, k, 1, 100)

⎛ 100 ⎞ ⎜ 5050 ⎟ e⎜ 338350 ⎟ ⎜ 25502500 ⎟ ⎝2050333330⎠

And here is a product:

∏(1 − 1/prime(n)^2, n, 1, 100000)

0.607927132988

Hint: To type the n-ary product symbol, ∏, type “\product” followed by space or a punctuation character. In this case, ( will do.

Hint: Instead of `∏`

, you may also use the synonym `product`

.