## Trapezoidal Rule Calculator

Your input: approximate the integral ∫10sin3(x)+1−−−−−−−−−√ dx ∫01sin3⁡(x)+1 dx using n=5 n=5 trapezoids. The trapezoidal rule states that ∫baf(x)dx≈Δx2(f(x0)+2f(x1)+2f(x2)+…+2f(xn−1)+f(xn)) ∫abf(x)dx≈Δx2(f(x0)+2f(x1)+2f(x2)+…+2f(xn−1)+f(xn)) , where Δx=b−an Δx=b−an .

## Simpson’s Rule Calculator

SOLUTION Your input: approximate the integral ∫101×5+7−−−−−√3 dx∫011×5+73 dx using n=4n=4 rectangles.    Now, we just evaluate the function at these endpoints: f(x0)=f(a)=f(0)=7237=0.52275795857471 f(x0)=f(a)=f(0)=7237=0.52275795857471   4f(x1)=4f(14)=3271692–√3(7169)23=2.09093460413808

## Kaomoji Japanese Emoticons

Kaomoji: Japanese Emoji. Kaomoji (顔文字) is a traditional Japanese emoticon form built up of Japanese letters and grammar punctuations, and are used to show excitement in texting and Online chatting. The word kaomoji is also known as Japanese emoticons

## Copy and Paste Faces

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