\int_{0}^{ {\x}} { {\t}^2}/\sqrt{ {\a}^2+ {\t}^2}} {\dt}= [AP EAPCET 23 May 2025 S1]

Correct Answer is : x2√a2+x2−a22Sinh−1xa

\frac{x}{2} \sqrt{a^2+x^2}+\log {| x+\sqrt{a^2+x^2} |}

\sqrt{a^2+x^2}-a^2 \sinh ^{-1} \frac{x}{a}

\frac{x}{2} \sqrt{a^2+x^2}+\frac{a^2}{4} \log {| x+\sqrt{a^2+x^2} |}

\frac{x}{2} \sqrt{a^2+x^2}-\frac{a^2}{2} {\Sinh}^{-1} \frac{x}{a}

Definite Integration

Section: Mathematics

Question : 10 of 54

Marks: +1, -0

∫

‌

√a2+t2

‌dt=

[AP EAPCET 23 May 2025 S1]

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