Copernicus's main contribution was to propose a heliocentric model for the solar system, i.e. one with the sun at the center instead of the earth. This was in contrast to the Ptolemaic models which placed the earth at the center and required complicated "epicycles" to describe why planets would wobble back and forth in the sky instead of moving in nice straight lines.
Calculus, on the other hand, was invented simultaneously and independently by Newton and Leibniz.
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Issac Newton and Gottfried Leibniz are the co-discovers of this system of mathematical analysis.
Integral calculus was invented in the 17th century with the independent discovery of the fundamental theorem of calculus by Newton and Leibniz.
Calculus was invented or rather can be detailed as back as 1820 B.C. when the Egyptians used it in order to calculate the volume of the pyramidal frustum
Calculus was invented to solve physics problems, so the importance of studying calculus is to solve physics problems.
What mathematical symbol? Different symbols were invented in different times and places.