TS EAMCET · Maths · Definite Integration
\(\int_0^{10}\left(5-\sqrt{10 x-x^2}\right) d x=\)
- A \(50-25 \pi\)
- B \((100-25 \pi)\)
- C \(\frac{1}{2}(100-25 \pi)\)
- D \(\frac{1}{4}(100-25 \pi)\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}(100-25 \pi)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } \\ & I=\int_0^{10} 5-\sqrt{\left.10 x-x^2\right)} d x, I=\int_0^{10}\left(5-\sqrt{(5)^2-(x-5)^2} d x\right. \\ & I=\left[5 x-\frac{x-5}{2} \sqrt{10 x-x^2}-\frac{25}{2} \sin ^{-1} \frac{x-5}{5}\right]_0^{10} \\ & I=\left(50-0-\frac{25}{2} \sin…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int_0^\pi \frac{1}{1+\sin x} d x\) is equal toTS EAMCET 2009 Medium
- If three dice are thrown at a time, then the probability of getting the sum of the numbers on them as a prime number isTS EAMCET 2025 Medium
- If the line \(2 x-y-4=0\) divides the line segment joining the points \((2,-1)\) and \((1,-4)\) at the point \((a, b)\) in the ratio \(m: n\) then \(4\left(a-b\left(\frac{m}{n}\right)^2\right)=\)TS EAMCET 2022 Easy
- If \(f(x)= \begin{cases}\frac{8}{x^3}-6 x, & \text { if } 0 \lt x \leq 1 \ \frac{x-1}{\sqrt{x}-1}, & \text { if } x\gt1\end{cases}\) is a real valued function, then at \(x=1, f\) isTS EAMCET 2024 Medium
- If the lines \(x+3 y-5=0,5 x+2 y-12=0\) and \(3 x-k y-1=0\) do not form a triangle, then a value of \(k\) isTS EAMCET 2019 Easy
- Let \(X\) and \(Y\) be two events of a sample space such that \(P(X)=\frac{1}{3}, P(X / Y)=\frac{1}{2}\) and \(P(Y / X)=\frac{2}{5}\) thenTS EAMCET 2020 Easy
More PYQs from TS EAMCET
- The number of ways in which \(\mathrm{n}\) boys and \(\mathrm{n}\) girls can be arranged in a row such that all the boys are together and all the girls are also together is equal toTS EAMCET 2023 Hard
- \(\frac{1}{\sin 250^{\circ}}+\frac{\sqrt{3}}{\cos 290^{\circ}}=\)TS EAMCET 2022 Easy
- At \(x=0, f(x)=\left\{\begin{array}{l}\frac{x}{|x|+2 x^2}, x \neq 0 \ k, \quad x=0\end{array}\right.\) isTS EAMCET 2020 Medium
- If \(x=\frac{\mathrm{t}^2}{1+\mathrm{t}^5}, y=\frac{2 \mathrm{t}^3}{1+\mathrm{t}^5}\) and \(\mathrm{t} \neq-1\) is a parameter then \(\frac{d y}{d x}=\)TS EAMCET 2025 Medium
- The angle between (100) and (110) planes of FCC lattice isTS EAMCET 2020 Easy
- \(\int_0^\pi \frac{x d x}{4 \cos ^2 x+9 \sin ^2 x}=\)TS EAMCET 2017 Hard