query: Why is antiderivative used to calculate the area under the curve?
positive_passages.docid: 67224
positive_passages.text: Why is the area under a curve the integral?
negative_passages.docid: 49984
negative_passages.text: Valid justification for algebraic manipulation of $\mathrm{d}y/\mathrm{d}x$?
negative_passages.docid: 2243
negative_passages.text: Check if antiderivative is elementary
negative_passages.docid: 69203
negative_passages.text: Calculus proof for the area of a circle
negative_passages.docid: 105248
negative_passages.text: Why is the gradient of implicit surface the normal vector (i.e. parallel to the normal line)?
negative_passages.docid: 12172
negative_passages.text: help me understand derivatives and their purpose
negative_passages.docid: 62135
negative_passages.text: Area under the graph of a convex function
negative_passages.docid: 87041
negative_passages.text: How to determine with certainty that a function has no elementary antiderivative?
negative_passages.docid: 25569
negative_passages.text: Intuitive understanding of the derivatives of $\sin x$ and $\cos x$
negative_passages.docid: 85764
negative_passages.text: Why is surface area not simply $2 \pi \int_{a}^{b} (y) dx$ instead of $2 \pi \int_a^b (y \cdot \sqrt{1 + y'^2}) dx$?
negative_passages.docid: 109182
negative_passages.text: Expressing the area of the cross section of a cylinder
negative_passages.docid: 5086
negative_passages.text: Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
negative_passages.docid: 108284
negative_passages.text: Integration and existence of an antiderivative
negative_passages.docid: 30507
negative_passages.text: What is the intuitive meaning of line integral with respect to x?
negative_passages.docid: 81228
negative_passages.text: Can I resubstitute polar coordinates after differentiation?
negative_passages.docid: 67907
negative_passages.text: Evaluating $\int_{-a}^a \frac{f(x)+1}{b^x+1}\,\mathrm dx$ for a $y$-axis symmetrical function $f$
negative_passages.docid: 103804
negative_passages.text: Why is $m$ used to denote slope?