AP EAMCET · Maths · Indefinite Integration
Let the equation of the curve passing through the point \((0,1)\) be given by \(y=\int x^3 e^{x^4} d x\). If the equation of the curve is written in the form \(x=f(y)\), then \(f(y)=\)
- A \(\log |4 y-3|\)
- B \((\log |4 y-3|)^{1 / 4}\)
- C \(\left(\log \left|\frac{3-4 y}{4}\right|\right)^{1 / 4}\)
- D \(\log \left|\frac{4 y-3}{4}\right|\)
Answer & Solution
Correct Answer
(B) \((\log |4 y-3|)^{1 / 4}\)
Step-by-step Solution
Detailed explanation
It is given that, \(y=\int x^3 e^{x^4} d x\) Let \(x^4=t \Rightarrow 4 x^3 d x=d t\) \(\therefore\) So, \(y=\frac{1}{4} \int e^t d t=\frac{e^t}{4}+C=\frac{e^{x^4}}{4}+C\) \(\because\) The curve \(y=\frac{e^{x^4}}{4}+C\) passes through point \((0,1)\), so…
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 \(A\) and \(B\) are two events such that \(P(B) \neq 0\) and \(P(B) \neq 1\), then \(P(\bar{A} \mid \bar{B})\) isAP EAMCET 2022 Easy
- An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting a total of odd number of points isAP EAMCET 2004 Medium
- The difference of the irrational roots of the equation \(x^5-5 x^4+9 x^3-9 x^2+5 x-1=0\) isAP EAMCET 2017 Hard
- If \(a x^2+2 h x y-2 a y^2+3 x+15 y-9=0\) represents a pair of lines intersecting at \((1,1)\), then ah \(=\)AP EAMCET 2025 Medium
- If the chord of contact of \(\mathrm{P}\left(x_1, y_1\right)\) with respect to the circle \(x^2+y^2=a^2\) meets the circle at \(\mathrm{A}\) and \(\mathrm{B}\); and if \(\lfloor \mathrm{AOB}=90^{\circ}\), then \(x_1^2+y_1^2=\)AP EAMCET 2017 Easy
- If a point \(\mathrm{R}(4, \mathrm{y}, \mathrm{z})\) lies on the line joining the points \(P(2,-3,4)\) and \(Q(8,0,10)\), then distance of \(R\) from origin isAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- Predict the correct order of rate of diffusion of the following molecules.AP EAMCET 2020 Easy
- Consider the following data:
The coefficient of variation of the above distribution of wages, if its standard deviation is 14.72 , isAP EAMCET 2017 Easy - In an \(\mathrm{AC}\) generator, the ends of the coil are connected toAP EAMCET 2020 Easy
- The walls of a closed cubical box of edge \(60 \mathrm{~cm}\) are made of material of thickness \(1 \mathrm{~mm}\) and thermal conductivity, \(4 \times 10^{-4} \mathrm{cal} \mathrm{s}^{-1} \mathrm{~cm}^{-1}{ }^{\circ} \mathrm{C}^{-1}\). The interior of the box is maintained \(1000^{\circ} \mathrm{C}\) above the outside temperature by a heater placed inside the box and connected across \(400 \mathrm{~V}\) DC supply. The resistance of the heater isAP EAMCET 2019 Hard
- \(\int_{-1}^{3 / 2}|x \sin \pi x| d x=\)AP EAMCET 2017 Medium
- Five equal resistances each ' 2 R ' are connected as shown in figure. A battery of ' \(V\) ' volts connected between \(A\) and B. Then current through FC is
AP EAMCET 2024 Hard