Integrals, NCERT Solutions & Previous Year Papers, Class 12th, Mathematics CBSE

INDEFINITE INTEGRALS Page 19.4 Ex.19.1 Q1. Answer : (i) ∫x4dx=x4+14+1+C =x55+C (ii) ∫x54dx=x54+154+1+C=49×94+C (iii) ∫x-5dx=x-5+1-5+1+C=-14x-4+C=-14×4+C (iv) ∫dxx3/2=∫x-3/2dx=x-32+1-32+1+C=x-12-12+C=-2x+C (v) ∫3xdx=3xln 3+C (vi) ∫dxx23=∫dxx2/3=∫x-2/3 dx=x-23+1-23+1+C=3×13+C (vii) ∫32 log3xdx=∫3log3 x2dx=∫x2dx=x33+C (viii) ∫logxx dx=∫1·dx=x+C Q2. Answer : (i) ∫1+cos 2x2dx ∫2 cos2x2dx ∴1+cos2A=2cos2A=∫cosx dx=sin x+C (ii) ∫1-cos 2x2dx =∫2sin2x2dx ∴1-cos 2x=2sin2x=∫sinx dx=-cos x+C Q3. Answer : ∫e6 log x-e5 […]

1. There will be total 10  MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

1. There will be total 5  MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

1. There will be total 5  MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

1. There will be total 10 MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative marking […]

1. There will be total 5  MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

1. There will be total 10  MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

1. There will be total 10  MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

1. There will be total 10 MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No […]

1. There will be total 10 MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No […]