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.