AP EAMCET · Maths · Definite Integration
\(\int_{-1}^4 \sqrt{\frac{4-x}{x+1}} d x=\)
- A 0
- B \(\frac{\pi}{2}\)
- C \(\frac{3 \pi}{2}\)
- D \(\frac{5 \pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{5 \pi}{2}\)
Step-by-step Solution
Detailed explanation
The integral is of the form \(\int_a^b \sqrt{\frac{b-x}{x-a}} dx\). The value of this integral is \(\frac{\pi}{2}(b-a)\). Given \(a = -1\) and \(b = 4\). \(= \frac{\pi}{2}(4 - (-1))\) \(= \frac{\pi}{2}(5)\)\(= \frac{5\pi}{2}\)
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
- If the lines \(x^2+2 x y-35 y^2-4 x+44 y\) \(-12=0\) and \(5 x+\lambda y-8=0\) are concurrent, then \(\lambda\) equalsAP EAMCET 2021 Easy
- The value of \(c\) such that the straight line joining the points \((0,3)\) and \((5,-2)\) is tangent to the curve \(y=\frac{c}{x+1}\) isAP EAMCET 2024 Easy
- All the letters of the word ANIMAL are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word ANIMAL is \(x\), then the permutation with rank \(x\), among the permutations obtained by permuting the letters of the word PERSON and arranging the permutations thus formed in dictionary order isAP EAMCET 2019 Medium
- A true statement among the following identities isAP EAMCET 2022 Medium
- If \(x^2+p x+1\) is a factor of \(a x^3+b x+c\), thenAP EAMCET 2021 Easy
- What is the value of \(x\) if the mean of \(8,6,7\), \(5, x\) and 4 is 7 ?AP EAMCET 2020 Easy
More PYQs from AP EAMCET
- The number of isomers of is:AP EAMCET 2020 Easy
- If the circles \((x+a)^2+(y+b)^2=a^2\) and \((x+c)^2+(y+d)^2=d^2\) cut orthogonally, then \(b(b-2 d)=\)AP EAMCET 2019 Easy
- Find the equation of pair of straight lines that bisect the angles between the lines represented by \(a x^2+2 h x y+b y^2=0\).AP EAMCET 2020 Medium
- \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+3 x^2-10 x-24=\) 0 . If \(\alpha(\beta+\gamma), \beta(\gamma+\alpha)\) and \(\gamma(\alpha+\beta)\) are the roots of the equation \(x^3+p x^2+q x+r=0\), then \(q=\)AP EAMCET 2024 Medium
- Given three vectors \(\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\), a vector in the plane of \(\mathbf{b}\) and \(\mathbf{c}\) whose projection on \(\mathbf{a}\) is of magnitude \(\sqrt{\frac{2}{3}}\) isAP EAMCET 2019 Medium
- A straight conductor of length \(4 \mathrm{~m}\) moves at a speed of \(10 \mathrm{~m} / \mathrm{s}\). When the conductor makes on angle of \(30^{\circ}\) with the direction of magnetic field of induction of \(0.1 \mathrm{~Wb}-\mathrm{m}^2\), then induced emf isAP EAMCET 2012 Easy