Evaluate the integral. \displaystyle \int \sin^{-1}x dx Evaluate each indefinite Integral. a) \int \frac{dx}{x^{\frac{2}{3 (2 + x^{\frac{1}{3)} b) \int \frac{5x^2 + 20x}{x^3 + 6x^2 + 4} dx Evaluate these integral: (a) \int 5 \frac{e^4 - x}{e^{6...
In summary, the given indefinite integral is equal to the absolute value of the difference between the square root of x and the square root of 1-x, and can be solved by splitting the integral into two parts and using the appropriate substitution for each part. ...
Evaluate each definite integral. a) \int_{1}^{2}(x^2-3)dx\\ b) \int_{1}^{4}3\sqrt t dt\\ Evaluate the definite integral. integral_0^pi/4 sin(t)/cos^2(t) dt Evaluate the definite integral. integral_{1 / {54^{1 / {18 csc (9 pi t) cot (9 pi t...
Evaluate the indefinite integral \int \frac{6x^3 + 4x^2 + 2}{x^2} \,dx Evaluate the indefinite integral \int (2x-1)^{100} dx. Evaluate the indefinite integral \int \frac{x^3 - 3x^2 + 5}{x-3} \,dx Evaluate the indefinite integral. \int 4...
Find each indefinite integral: a. \ \int x(x^3 + 2) dx\b.\ \int \frac {1}{4x^2} \ dx.\c. \ \int(4x - csc^2 x) dx. Evaluate the integral. integral 0^1 integral square root 3 z ^1 integral 0^ ln 3 fraction pi e^2x sin pi y^2 y^2 dx dy dz ...
Evaluate the following integrals :∫(x3+8)(x−1)x2−2x+4dx View Solution Evaluate the following integral:∫21|x−3|dx View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and ...
Step 4: Simplify the IntegralNow, we can simplify the integrand: I=∫(t−3+3t−1t2)dt. Step 5: Integrate Term by TermNow we integrate each term separately: 1. ∫tdt=t222. ∫−3dt=−3t3. ∫3tdt=3ln|t|4. ∫−1t2dt=1t Putting it all together, we have: I=t22−3t...
Use substitution to find each indefinite integral. (a) integral r Squareroot {r^2 +2} dr, (b) integral (1 - x) e^{2x - x^2} dx, (c) integral {-4x}/{x^2 + 3} dx. Evaluate the following indefinite integral. integral (e^{-6 x} + e^{x / 5}) dx ...
Solve the power of each term of the integrand. {eq}\b... Learn more about this topic: Indefinite Integrals as Anti Derivatives from Chapter 12/ Lesson 11 17K Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify indi...
Evaluate each integral. \int \frac{x^2-1}{x^3+x}dx (Hint: use a partial fraction). Express the integrand as a sum of partial fractions and evaluate the integral. 1. \int \frac { 4 x + 46 } { x ^ { 2 }...