Mathematics

Integrate $$\int (1+y^{2})dx$$


SOLUTION
$$\int{\left( 1 + {y}^{2} \right) \; dx}$$
Since the integration is w.r.t. $$x$$, thus the $$\left( 1 + {y}^{2} \right)$$ is constant here.
Therefore,
$$\int{\left( 1 + {y}^{2} \right) \; dx}$$
$$= \left( 1 + {y}^{2} \right) \int{dx}$$
$$= \left( 1 + {y}^{2} \right) x + C$$
Thus,
$$\int{\left( 1 + {y}^{2} \right) \; dx} = \left( 1 + {y}^{2} \right) x + C$$
Hence the correct answer is $$\left( 1 + {y}^{2} \right) x + C$$.
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Subjective Medium Published on 17th 09, 2020
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