AP EAMCET · Maths · Indefinite Integration
Suppose that \(f\) and \(g\) are integrable on \([a, b]\), then \(f+g\) is integrable on ......... .
- A \((a, b)\)
- B Cannot comment
- C \([a, b]\)
- D Range of \(f+g\)
Answer & Solution
Correct Answer
(C) \([a, b]\)
Step-by-step Solution
Detailed explanation
As \(f\) and \(g\) are integrable on \([a, b]\), then \(\int_{x_1}^{x_2} f(x) d x\) and \(\int_{x_1}^{x_2} g(x) d x\) exists for every value of \(x_1, x_2 \in[a, b]\), then \(\int_{x_1}^{x_2} f(x) d x+\int_{x_1}^{x_2} g(x) d x=\int_{x_1}^{x_2}(f+g)(x) d x\) Also exists for…
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
- The point to which the origin is to be shifted to eliminate \(x\) and \(y\) terms of the equation \(4 x^2+9 y^2-8 x+36 y+4=0\) isAP EAMCET 2017 Medium
- If the sum of two roots of the equation \(x^4+2 x^3-7 x^2-8 x+12=0\) is zero, then the sum of the squares of the other two roots isAP EAMCET 2025 Medium
- Let \(\mathbf{A}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) and \(\mathbf{B}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\). If \(C\) is a vector such that \(\mathbf{A} \cdot \mathbf{C}=|\mathbf{C}|,|\mathbf{C}-\mathbf{A}|=2 \sqrt{2}\) and the angle between \(\mathbf{A} \times \mathbf{B}\) and \(\mathbf{C}\) is \(30^{\circ}\), then the value of \(|(\mathbf{A} \times \mathbf{B}) \times \mathbf{C}|\) isAP EAMCET 2019 Medium
- If a circle of radius 4 cm passes through the foci of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{4}=1\) and concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola isAP EAMCET 2024 Easy
- If the first three terms in the binomial expansion of \((1+b x)^n\) in ascending powers of \(x\) are \(1,6 x\) and \(6 x^2\) respectively then \(b+n=\)AP EAMCET 2017 Medium
- The cosine of the angle \(A\) of the triangle with vertices \(A(1,-1,2), B(6,11,2), C(1,2,6)\) isAP EAMCET 2007 Easy
More PYQs from AP EAMCET
- The direction cosines of the line joining the points and areAP EAMCET 2021 Easy
- A body is projected up with a velocity equal to \(\frac{3}{4}\) th of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth \(=R\) )AP EAMCET 2002 Easy
- The empirical formula weight of ' \(Z\) ' in the given reaction sequence is
n-propyl bromide \(\xrightarrow[\text { Dry ether }]{\mathrm{Na}} \mathrm{X} \xrightarrow[\substack{773 \mathrm{~K} \\ 20 \mathrm{~atm}}]{\mathrm{V}_2 \mathrm{O}_5} \mathrm{Y} \xrightarrow[\substack{\mathrm{UV} \\ 500 \mathrm{~K}}]{\mathrm{Cl}_2} \mathrm{Z}\)AP EAMCET 2025 Medium - A satellite revolving around a planet has orbital velocity \(10 \mathrm{~km} / \mathrm{s}\). The additional velocity required for the satellite to escape from the gravitational field of the planet isAP EAMCET 2015 Medium
- The ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(b>a)\) and the parabola \(y^2=4 a x\) cut at right angles. If \(e\) is the eccentricity of the ellipse, then \(2 e^2=\)AP EAMCET 2019 Easy
- In , suppose the radius of the circle opposite to an angle is denoted by , similarly angle angle If is the radius of inscribed circle then, what is the value ofAP EAMCET 2021 Medium